A nonlinear coupled wing model subject to unknown external disturbances is proposed in this paper. Since the model is modeled by partial differential equations, the traditional control design scheme based on the ordinary differential equation model is not applicable, and the control law design becomes very complex. In this paper, a new antidisturbance boundary control scheme based on a finite time convergent disturbance observer is proposed. The control laws are designed based on the new disturbance observers to make the (...) external disturbance errors converge to zero in a finite time and ensure the uniformly bounded stability of the controlled system. Finally, the effectiveness of the controllers and the finite-time convergence of disturbance errors are verified by the simulation and comparison. (shrink)

With contributions from a number of pioneering researchers in the field, this collection is aimed not only at researchers and scientists in nonlinear dynamics but also at a broader audience interested in understanding and exploring how modern chaos theory has developed since the days of Poincaré. This book was motivated by and is an outcome of the CHAOS 2015 meeting held at the Henri Poincaré Institute in Paris, which provided a perfect opportunity to gain inspiration and discuss new perspectives (...) on the history, development and modern aspects of chaos theory. Henri Poincaré is remembered as a great mind in mathematics, physics and astronomy. His works, well beyond their rigorous mathematical and analytical style, are known for their deep insights into science and research in general, and the philosophy of science in particular. The Poincaré conjecture (only proved in 2006) along with his work on the three-body problem are considered to be the foundation of modern chaos theory. (shrink)

Nonlinear time series denoising is the prerequisite for extracting effective information from observation sequence. An effective chaotic signal denoising method not only has a good signal-to-noise ratio enhancement performance, but also can remain as a good unpredictable denoised signal. However, the inherent characteristics of chaos, such as extreme sensitivity to initial values and broadband spectrum, pose challenges for noise reduction of polluted chaotic signals. To address these issues, an adaptive smoothing multiscale morphological filtering is proposed to reconstruct chaotic signals. (...) In the process of noise reduction for contaminated chaotic signals, firstly, a multiscale morphological filter is constructed adaptively according to the multiscale permutation entropy of morphological filter residuals, and the contaminated signals are filtered. Secondly, the weight coefficients of scale structural element are calculated by the residual sum of squares operation, and the chaotic signals are reconstructed. Finally, the resampled filter signals are smoothed by cubic B-spline interpolation operation. In the experiment, the Lorenz signal with white Gaussian noise, the measured sunspot, and the chaotic vibration signal are reconstructed by four comparison methods. The test results show that the proposed ASMMF method has obvious advantages in noise suppression and topological trajectory restoration. (shrink)

Electromechanical actuators are more and more widely used as actuation devices in flight control system of aircrafts and helicopters. The reliability of EMAs is vital because it will cause serious accidents if the malfunction of EMAs occurs, so it is significant to detect and diagnose the fault of EMAs timely. However, EMAs often run under variable conditions in realistic environment, and the vibration signals of EMAs are nonlinear and nonstationary, which make it difficult to effectively achieve fault diagnosis. (...) This paper proposed a fault diagnosis method of electromechanical actuators based on variational mode decomposition multifractal detrended fluctuation analysis and probabilistic neural network. First, the vibration signals were decomposed by VMD into a number of intrinsic mode functions. Second, the multifractal features hidden in IMFs were extracted by using MFDFA, and the generalized Hurst exponents were selected as the feature vectors. Then, the principal component analysis was introduced to realize dimension reduction of the extracted feature vectors. Finally, the probabilistic neural network was utilized to classify the fault modes. The experimental results show that this method can effectively achieve the fault diagnosis of EMAs even under diffident working conditions. Simultaneously, the diagnosis performance of the proposed method in this paper has an advantage over that of EMD-MFDFA method for feature extraction. (shrink)

The suspension system is referred to as the set of springs, shock absorbers, and linkages that connect the car to the wheel system. The main purpose of the suspension system is to provide comfort for the passengers, which is created by reducing the effects of road bumpiness. It is worth noting that reducing the effects of such vibrations also diminishes the noise and undesirable sound as well as the effects of fatigue on mechanical parts of the vehicle. Due to the (...) importance of the abovementioned issues, the objective of this article is to reduce such vibrations on the car by implementing an active control method on the suspension system. For this purpose, a conventional first-order sliding mode controller has been designed for stochastic control of the quarter-car model. It is noteworthy that this controller has a significant ability to overcome the stochastic effects, uncertainty, and deal with nonlinear factors. To design a controller, the governing dynamical equation of the quarter-car system has been presented by considering the nonlinear terms in the springs and shock absorber, as well as taking into account the uncertainty factors in the system and the actuator. The design process of the sliding mode controller has been presented and its stability has been investigated in terms of the Lyapunov stability. In the current research, road surface variations are considered as Gaussian white noise. The dynamical system behavior for controlled and uncontrolled situations has been simulated and the extracted results have been presented. Besides, the effects of existing uncertainty in the suspension system and actuator have been evaluated and controller robustness has been checked. Also, the obtained quantitative and qualitative compressions have been presented. Moreover, the effect of controller parameters on the basin of attraction set and its extensiveness has been assessed. The achieved results have indicated the good performance and significant robustness of the designed controller to stabilize the suspension system and mitigate the effects of road bumpiness in the presence of uncertainty and noise factors. (shrink)

The problem of adaptive finite-time fault-tolerant control and output constraints for a class of uncertain nonlinear half-vehicle active suspension systems are investigated in this work. Markovian variables are used to denote in terms of different random actuators failures. In adaptive backstepping design procedure, barrier Lyapunov functions are adopted to constrain vertical motion and pitch motion to suppress the vibrations. Unknown functions and coefficients are approximated by the neural network. Assisted by the stochastic practical finite-time theory and FTC theory, the (...) proposed controller can ensure systems achieve stability in a finite time. Meanwhile, displacement and pitch angle in systems would not violate their maximum values, which imply both ride comfort and safety have been enhanced. In addition, all the signals in the closed-loop systems can be guaranteed to be semiglobal finite-time stable in probability. The simulation results illustrate the validity of the established scheme. (shrink)

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to (...) the nonlinear soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

The nonlinearity of a composite system, whereby certain of its features (including powers and behaviors) cannot be seen as linear or other broadly additive combinations of features of the system's composing entities, has been frequently seen as a mark of metaphysical emergence, coupling the dependence of a composite system on an underlying system of composing entities with the composite system's ontological autonomy from its underlying system. But why think that nonlinearity is a mark of emergence, and moreover, of metaphysical rather (...) than merely epistemological emergence? Are there diverse ways in which nonlinearity might enter into an account of properly metaphysical emergence? And what are the prospects for there actually being phenomena that are metaphysically emergent in any available sense? Here I explore the mutual bearing of nonlinearity and metaphysical emergence, with an eye towards answering these and related questions. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be (...) the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

The models of the electric charge and magnetic moment are presented based on the nonlinear response of a vacuum on the applied electric and magnetic fields. The model of the electric charge contains one parameter—the radius of charge—and predicts one value of the electric charge for all elementary particles independently on the value of this radius. Different values of this parameter for the electron are discussed.

Ever wonder if it is possible to construct a numeric scale for environmental variables, like one does for the temperature? This paper is an attempt to construct one. There are two main parts: section “Statistical Analysis of Variations” presents a general statistical strategy for environmental factor selection. Section “Nonlinear Analytical Geometric Model of Variations” develops an analytical geometric representation of system variations in response to environmental changes. The model is used to quantify the effects of environmental interactions. The paper (...) treats only one-dimensional case, however, the derivation of the case of multiple independent factors follows immediately. The general method developed in this paper may prove applicable to many different fields, such as extensions beyond classical physics, economics, and other sciences. Section “Conclusion” provides an illustration of applications, examples and implications of the results. (shrink)

More than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics.Following in the wake of his groundbreaking War in the Age of Intelligent Machines, Manuel De Landa presents a radical synthesis of historical development over the last one thousand years. More (...) than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics. Working against prevailing attitudes that see history as an arena of texts, discourses, ideologies, and metaphors, De Landa traces the concrete movements and interplays of matter and energy through human populations in the last millennium. De Landa attacks three domains that have given shape to human societies: economics, biology, and linguistics. In every case, what one sees is the self-directed processes of matter and energy interacting with the whim and will of human history itself to form a panoramic vision of the West free of rigid teleology and naive notions of progress, and even more important, free of any deterministic source of its urban, institutional, and technological forms. Rather, the source of all concrete forms in the West's history are shown to derive from internal morphogenetic capabilities that lie within the flow of matter-energy itself. (shrink)

The challenges posed by chronic illness have pointed out to epidemiologists the multifactorial complex nature of disease causality. This notion has been referred to as a web of causality. This web extends theoretically beyond risk markers. It includes determinants of emergence/non-emergence of disease. This web of determinants is a form of complex system. Due to its complexity, the determinants within such system are not linked to each others in a linear, predictable manner only. Predictability is possible only on a short-term (...) basis, and unpredictability sets in over the long run. Understanding such a system of determinants calls for articulation and testing of complex models which synthesize our knowledge of multiple determinants at many scales, both biological and otherwise. Given the complexity of this web and existing knowledge about the nonlinearity of such systems, the following question is posed: Can the challenge of studying causality be adequately addressed if emphasis continues to be placed on using tools and methods that are geared towards looking at such system from a linear paradigm? Or is it time to add to the epidemiologic research agenda the notion of nonlinearity and its relevant form of analytical approaches that are being tested in other disciplines? Furthermore, the question posed here applies as well to the study of determinants of health. Addressing determinants of heath adds further complexity to our task. (shrink)

Today a change is imperative in approaching global problems: what is needed is not arm-twisting and power politics, but searching for ways of co-evolution in the complex social and geopolitical systems of the world. The modern theory of self-organization of complex systems provides us with an understanding of the possible forms of coexistence of heterogeneous social and geopolitical structures at different stages of development regarding the different paths of their sustainable co-evolutionary development. The theory argues that the evolutionary channel to (...) the observed increasing complexity is extremely narrow and only certain discrete spectra of relatively stable self-maintained structures are feasible in complex systems. There exists a restricted set of ways of assembling a complex evolutionary whole from diverse parts. The law of nonlinear synthesis of complex structures reads: the integration of structures in more complex ones occurs due to the establishment of a common tempo of their evolution. On the basis of the theory, we can see not only desirable but also attainable futures. (shrink)

A previous model for treating electromagnetic nonlinear wave systems is examined in the context of wave mechanics. It is shown that nonlinear wave mechanics implies harmonic generation of new quasiparticle wave functions, which are absent in linear systems. The phenomenon is interpreted in terms of pair (and higher order ensembles) coherence of the interacting particles. The implications are far-reaching, and the present approach might contribute toward a common basis for diverse physical phenomena involving nonlinearity. An intimate relationship connecting (...) coherence, nonlocal interaction, and nonlinearity has been previously noticed in the physics of superconductivity. It is shown here that all these ingredients are consistently contained in the present formalism. The present theory may contribute to elucidate a controversial theory proposed by Panarella, who claims to have measured high-energy photons due to high-intensity laser radiation, which cannot be predicted on the basis of linear quantum theory. Panarella explains the new phenomena by stipulating a nonlinear intensity-dependent photon energy. It is argued here that nonlinearity, manifested in the presence of high intensity, may give rise to high- and low-energy photons, the so-called “effective” and “tired” photons, respectively. However, the present explanation does not involve ad hoc assumptions regarding the foundations of quantum theory. In analogy with the electrodynamic model, the present theory leads to particulate self-focusing in high-density streams of particles. Since such particulate beams are currently under consideration in connection with fusion reactions, this might be of future interest. (shrink)

B a c k g r o u n d. Considering a scientific truth as a process is connected with the understanding a concrete truth as unity of absolute and relative moments of such process. Beginning by Hegel, truth was regarded as linear process with final point of its development. It was absolute truth, as return of absolute idea to itself in absolute spirit by Hegel. It was the third world by Popper as the world of objective truth. Ukrainian philosopher (...) Pavlo Kopnin opened development of truth for future, eliminating from it the final point in his materialistic interpretation of the truth as a process. However, such process was still regarded as linear process. It was natural for the stage of linear science. As I have already wrote (Dobronravova, 2017), modern stage of nonlinear science actualizes the considering of a scientific truth as nonlinear process. In situation of many variants of nonlinear dynamics the understanding of concrete truth needs to be updated. Such updating is the goal of the article. M e t h o d s. Dialectic method in addition to scientific realism is the most natural approach to research the modern nonlinear science. Methodologic conception of genetic constructivism by V. Stepin is foundation to consider the relations between theoretical and empirical levels of nonlinear knowledge. Criticism of correspondent conception of truth in internal realism by H.Putnam is initiative position in looking for right epistemolology of nonlinear science. Concrete truth as nonlinear process means the description of real nonlinear dynamics with knowledge about a choice, made by a self-organizing system between alternatives in bifurcation point. Nonlinear theories reconstruct few options of further development for nonlinear system. To explain a real situation in certain moment of such development means to describe the real choices by system in points of branching the possibilities. It means that nonlinear science becomes historical one that describes irreversible change of events. Methodologically it means the restriction for claim to repeat the results of empirical checking the predictions of theory, because of choice by chance in bifurcation points. This claim can work for nonlinear medium if different options can be realized in it simultaneously (like Benar's cells in layer of heated liquid or different parties in democratic societies). Otherwise things are going in the situations of historical kind, where the irreversible choice between alternatives has place (like historical choice between right-hand and left-hand traffic in different countries). Repetitions in empirical checking the predicted variants are not possible in principle because of random nature of choice in bifurcation points. R e s u l t s. Non-linear physical theories are descriptive, just like biological, geological and geographic theories. So arrogant condemnation of such theories by physicists and philosophers of science who took physics as a sample in many previous years founded on misunderstanding the specificity of different kinds of theories and their objects. Logical structure of explanation and prediction are not the same in non-linear theories. Non-linear theory can predict a set of possibilities but not the realization of certain one in certain moment. Concrete truth can be justified if human intervention provides the realization of special condition to choose selected variant. C o n c l u s i o n s. We have to understand that such task is more complicated, if we take into account the quantitative way to solve the nonlinear equations. The chain of iterations in approximate solution of such equations can rather give computer simulation of non-linear dynamics. Exact prediction with iteration formula of each next step of unfolding non-linear dynamics, does not guarantee the long scale prediction of complex nonlinear system state. It does not mean that knowledge we got about nonlinear phenomena are not useful for human practice. Thus, the change of dimension in fractal structures of "noise" in cardiograms lets to admit the first signs of heart illness and to cure heart in time. Meteorologists can warn pilots about oncoming storm, defining speed of rising flows in atmosphere by fractal dimension of pictures on the screen of radar. Those are the predictions in nonlinear science. Are they the proofs of concrete truth? Perhaps, yes, they are if we recall old formulation about practice as criteria of truth. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 229-234 [Access article in PDF] Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View Gordon Globus Keywords nonlinear dynamics, modernity, postmodernity, quantum brain theory, free will, self-organization, autopoiesis, autorhoesis Although nonlinear dynamical conceptu-alizations have been applied to psychia-try for over 20 years,1 they have not had significant impact on the field. Unfortunately Heinrichs' very thoughtful contribution to the (...) discussion is unlikely to move such disinterest. Pragmatically successful paradigms in the phase of Kuhnian "normal science" are highly resistant to change. There is no crisis that besets triumphalist biological psychiatry that might lead to clinical or scientific revolution. At the same time, as I suggest at the end of this commentary, the ideas of nonlinear dynamics may not be revolutionary enough, remaining staunchly within the framework of modernity.In what follows I discuss four issues related to Heinrichs' article. First, I try to enrich his presentation of nonlinear dynamics by bringing in the role of self-organization in the evolution of nonlinear dynamical brain systems and by making the nonlinear dynamics "tunable." Second, I discuss whether Heinrichs succeeds in avoiding the dualism of the biopsychosocial model that he criticizes. Third, I look at the issue of "free will," which Heinrichs would understandably like to avoid. Finally, I mention a new form of dynamics, namely thermofield dynamics, which I think is more promising than nonlinear dynamics. Self-Organizing Self-Tuning Nonlinear Dynamical Systems In the case of psychiatry, we are not considering nonlinear dynamical systems like the weather or an ecosystem, but the brain's neural networks in terms of nonlinear dynamics with all its chaos. There is a principle of such systems of neural networks that Heinrichs does not bring out, although it is extremely important for them. These systems are self-organizing under a Hamiltonian principle of "least energy." To use Hopfield and Tank's (1986) terms, nonlinear dynamical neural networks self-organize toward attractors that minimize the "computational energy" of the system, or for Smolensky (1988), self-organize toward "harmony," or for Globus (1995, 2003), in a Heideggerian vein, self-organize to maximize "belonging-together." In this elaborated framework, rational deliberation is one constraint among many on a self-organizing nonlinear dynamical process. [End Page 229]Heinrichs brings out beautifully the nonlinear dynamical way of thinking clinically. This is not the dynamics of mechanistic psychodynamics, which features psychological forces in vectorial conflict—id versus superego and their compromises—but a flowing evolution of states in which small changes in initial state may have large effects (nonlinearity) on the state trajectory. To live a life is often to feel surprise, which nonlinear dynamics with its chaotic regimes well portrays.But there is a way that classical Freud and nonlinear dynamical neural networks do come together—in the "economics," discharges and conservations of libidinal energy, expenditures and credits in Derrida's (1978) accounting. Heinrichs does not mention this similarity. The economic principles differ between Freud's late nineteenth-century thermodynamics and Heinrichs' late twentieth-century nonlinear dynamics, it is true, but it is all economics.Freud called this economic functioning the "pleasure principle" in which "libido" seeks to discharge its instinctual energy store, reducing the level of instinctual tension. This "primary process" proceeds to an attractor by the quickest, most direct way possible, whereas the "secondary process" defers reduction in instinctual tension, subjecting the primary process to thought. Self-organizing directly to the attractor is the primary process with which the secondary process interferes, introducing deferral.The economy of nonlinear dynamics pictures a "landscape," a variegated topography with peaks and valleys. Each point on the topography represents a state. Peak points are repellors—for example, states in which the phobic object is approached—and the lowest points of the valleys are attractors—for example, obsessions and compulsions. The path of occupied states self-organizes away from repellors and toward attractors. This topography is an energy landscape. Its dynamics spontaneously tends—"self-organizes"—toward least energy/high-constraint satisfaction. Freud's pleasure principle is just the Hamiltonian least energy... (shrink)

Using the genetic algorithm and fuzzy logic, this study presents a nonlinear approach to the evaluation of biofunctional intelligence. According to the biofunctional model, intelligence may be viewed as a multisource phenomenon resulting in part from the interaction of learning processes and sources of self-regulation. Learning processes are regulated by three sources of control , producing three subprocesses for each learning process. This paper examines the role of five such subprocesses as contributors to intelligence. Fuzzy logic captures the fuzzy (...) nature of human intelligence with GA providing a method for determining and optimizing the contribution of these learning subprocesses. (shrink)

Study of Advaita Vedanta, compared to the philosophy of Superstring theories of modern physics.

The use of upper limb vibration during exercise and rehabilitation continues to gain popularity as a modality to improve function and performance. Currently, a lack of knowledge of the pathways being altered during ULV limits its effective implementation. Therefore, the aim of this study was to investigate whether indirect ULV modulates transmission along spinal and corticospinal pathways that control the human forearm. All measures were assessed under CONTROL and ULV conditions while participants maintained a small contraction of the right (...) flexor carpi radialis muscle. To assess spinal pathways, Hoffmann reflexes elicited by stimulation of the median nerve were recorded from FCR with motor response amplitudes matched between conditions. An H-reflex conditioning paradigm was also used to assess changes in presynaptic inhibition by stimulating the superficial radial nerve 37 ms prior to median nerve stimulation. Cutaneous reflexes in FCR elicited by stimulation of the SR nerve at the wrist were also recorded. To assess corticospinal pathways, motor evoked potentials elicited by transcranial magnetic stimulation of the contralateral motor cortex were recorded from the right FCR and biceps brachii. ULV significantly reduced H-reflex amplitude by 15.7% for both conditioned and unconditioned reflexes. Therefore, ULV inhibits cutaneous and H-reflex transmission without influencing corticospinal excitability of the forearm flexors suggesting increased presynaptic inhibition of afferent transmission as a likely mechanism. A general increase in inhibition of spinal pathways with ULV may have important implications for improving rehabilitation for individuals with spasticity. (shrink)

With renewable energy being increasingly connected to power grids, pumped storage plants play a very important role in restraining the fluctuation of power grids. However, conventional control strategy could not adapt well to the different control tasks. This paper proposes an intelligent nonlinear model predictive control strategy, in which hydraulic-mechanical and electrical subsystems are combined in a synchronous control framework. A newly proposed online sequential extreme learning machine algorithm with forgetting factor is introduced to learn the dynamic behaviors of (...) the coupling system. Specifically, the initial learning parameters are optimized by prior-knowledge learning and a new self-adaptive adjustment strategy is also put forward. Subsequently, the stair-like control strategy and artificial sheep algorithm are used in rolling the optimization mechanism to replace the existing complex differential geometric solutions. Comparative experiments are carried out under different working conditions based on a PSP in China. The results show that the influence from coupling factors can be considerable and the proposed MPC strategy indicates superiority in voltage and load adjustment as well as the frequency oscillation suppression. (shrink)

Although one can endorse the complexity of the data and processes that Phillips & Singer (P&S) review, their mathematical suggestions can be compared critically with cases in nonlinear psychophysics, where the theoretician is faced with analogous problems. Owing to P&S's failure adequately to recognise both the intricate properties of nonlinear dynamics in networks and the constraints of metabolic demands on the temporal generation of patterns in biological nets their conclusions fail to meet the problems they properly address.

We study the conditions under which increasing risk raises the optimal control variable when the budget constraint is nonlinear. In contrast to the case when the budget constraint is linear, nonlinearities alter the risk attitudes of the economic agent; that is, the agent’s risk behavior is driven by the interaction between the shape of the utility function and the shape of the budget constraint. This paper complements the classical literature with linear payoff functions in two important ways. First, we (...) derive necessary and sufficient conditions for unambiguous comparative statics of changes in risk when the budget constraint is nonlinear. Second, we highlight the critical role of the coefficients of technological improvement and cross-prudence in technology derived from the nonlinear budget constraint in a similar form to that in which the coefficient of relative risk aversion and the coefficient of relative prudence are derived from the utility function. We show several applications of this theory, including the worker’s decision to work in-person during a pandemic. (shrink)

The modern conception of enactive cognition is under discussion from the standpoint concerning the notions of nonlinear dynamics and synergetics. The contribution of Francisco Varela and his precursors is considered. It is shown that the perceptual and mental processes are bound up with the “architecture” of human body and nonlinear and circular connecting links between the subject of cognition and the world constructed by him can be metaphorically called a nonlinear cobweb of cognition. Cognition is an autopoietic (...) activity because it is directed to the search of elements that are missed; it serves to completing integral structures. (shrink)

Study of electroencephalographic brain activity in behaving animals has guided development of a model for the self-organization of goal-directed behavior. Synthesis of a dynamical representation of brain function is based in the concept of intentionality as the organizing principle of animal and human behavior. The constructions of patterns of brain activity constitute meaning and not information or representations. The three accepted meanings of intention: "aboutness," goal-seeking, and wound healing, can be incorporated into the dynamics of meaningful behavior, centered in the (...) limbic system interacting with the sensory and motor systems. Evidence is noted for the maintenance in cortical neuropil of a felt work of synaptic connections, that have incorporated past experience by changes in learning, and that act as a unified whole in shaping each intentional action at each moment. This constitutes the intentional structure of the brain. Meaning is a focus having a place without edges in this structure. The focus continually moves through it along a chaotic trajectory; the meaning occupies the whole structure. In this view, consciousness is the active state of an intentional structure, and awareness is the subjective aspect of the shifting focus. (shrink)

This article proposes that the propagation of vibrations could serve as a better model for understanding the transmission of affect than the flow, circulation or movement of bodies by which it is most often theorized. The vibrations (or idiomatically ‘vibes’) among the sound system audience (or ‘crowd’) on a night out on the dancehall scene in Kingston, Jamaica, provide an example. Counting the repeating frequencies of these vibrations in a methodology inspired by Lefebvre’s rhythmanalysis results in a Frequency Spectrogram. This (...) ranges from the sociocultural frequencies of nightly, weekly and seasonal cycles and circulations of musical style and fashion, to the material frequencies of the amplitudes and timbres of sound itself, with reggae’s signature low-pitched bass-line, to the corporeal frequencies of the flesh and blood of the dancehall ‘crowd’, pulsating with heartbeats and kinetic dance rhythms. The vibration model then addresses the intensities of affect in terms of auditory amplitudes, as with sonic dominance; feelings as frequencies; and the distinctive meaning of affect as timbre. This aims to encourage the radical impulse of the idea of affect to abandon the traditional envelope of the autonomous, self-consistent, rational individual. The meaning of affect is thus located in the ratio, proportions and patterning of vibrations, that is, outside the discourse of emotions or representation of feelings. (shrink)

We humans and other animals continuously construct and main- tain our grasp of the world by using astonishingly small snippets of sensory information. Recent studies in nonlinear brain dynamics have shown how this occurs: brains imagine possible futures and seek and use sensory stimulation to select among them as guides for chosen actions. On the one hand the scientific explanation of the dynamics is inaccessible to most of us. On the other hand the philosophical foundation from which the sciences (...) grew is accessible through the work of one of its originators, Thomas Aquinas. The core concept of intention in Aquinas is the inviolable unity of mind, brain and body. All that we know we have constructed within ourselves from the unintelligible fragments of energy impacting our senses as we move our bodies through the world. This process of intention is transi- tive in the outward thrust of the body in search of desired future states; it is intransitive in the dynamic construction of predictions of the states in the sensory cortices by which we recognize suc- cess or failure in achievement. The process is phenomenologically experienced in the action-perception cycle. Enactment is through the serial creation of neurodynamic activity patterns in brains, by which the self of mind-brain-body comes to know the world first by shaping the self to an approximation of the sought-for input, and then by assimilating those shapes into knowledge and meaning. This conception of the self as closed, autonomous, and self- organizing, devised over 700 years ago and shelved by Descartes, Leibniz and Spinoza 300 years ago, is now re-emerging in philos- ophy and re-establishes the meaning of intention in its original sense. The core Aquinian concept of the unity of brain, body and soul/mind, which had been abandoned by mechanists and replaced by Brentano and Husserl using the duality inherent in representa- tionalism, has been revived by Heidegger and Merleau-Ponty, but in phenomenological terms that are opaque to neurscientists. In my experience there is no extant philosophical system than that of Aquinas that better fits with the new _ndings in nonlinear brain dynamics. Therefore, a detailed reading and transcription of basic terms is warranted, comparing in both directions the significance of key words across 700 years from medieval metaphysics to 21st century brain dynamics. (shrink)

The present article deals with an observer design for nonlinear vehicle lateral dynamics. The contributions of the article concern the nonconsideration of any force model and the consideration that the longitudinal velocity is time varying, which is more realistic than the assumption that it is constant. The vehicle model is then represented by an exact Takagi–Sugeno model via the sector nonlinearity transformation. A proportional multiple integral observer based on the TS model is designed to estimate simultaneously the state vector (...) and the unknown input. The convergence conditions of the estimation error are expressed under LMI formulation using the Lyapunov theory, which guaranties a bounded error. Simulations are carried out for comparison between the conventional PI observer, the enhanced PI observer, and the PMI observer. Finally, experimental results are provided to illustrate the performances of the proposed PMI observer. (shrink)

Vitalism, from a physicist's standpoint, suggests the introduction of nonlinear transformations in Hilbert space. Two such transformations are introduced and studied in some detail. They are hard to detect by conventional experiments, although they may be very important for living organisms. They can, however, give rise to nonlocal effects, and thus provide a possible physical basis for some parapsychological phenomena, in particular precognition.

Behaviors of chaotic systems are unpredictable. Chaotic systems are deterministic, their evolutions being governed by dynamical equations. Are the two statements contradictory? They are not, because the theory of chaos encompasses two levels of description. On a higher level, unpredictability appears as an emergent property of systems that are predictable on a lower level. In this talk, we examine the structure of dynamical theories to see how they employ multiple descriptive levels to explain chaos, bifurcation, and other complexities of (...) class='Hi'>nonlinear systems.. (shrink)

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link (...) these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

This paper presents a method of measuring the vibration patterns on facial surfaces by using a scanning laser Doppler vibrometer (LDV). The surfaces of the face, neck, and body vibrate during phonation and, according to Titze ( 2001 ), these vibrations occur when aerodynamic energy is efficiently converted into acoustic energy at the glottis. A vocalist's vibration velocity patterns may therefore indicate his or her phonatory status or singing skills. LDVs enable laser-based non-contact measurement of the vibration (...) velocity and displacement of a certain point on a vibrating object, and scanning LDVs permit multipoint measurements. The benefits of scanning LDVs originate from the facts that they do not affect the vibrations of measured objects and that they can rapidly measure the vibration patterns across planes. A case study is presented herein to demonstrate the method of measuring vibration velocity patterns with a scanning LDV. The objective of the experiment was to measure the vibration velocity differences between the modal and falsetto registers while three professional soprano singers sang sustained vowels at four pitch frequencies. The results suggest that there is a possibility that pitch frequency are correlated with vibration velocity. However, further investigations are necessary to clarify the relationships between vibration velocity patterns and phonation status and singing skills. (shrink)

The book describes the features that vibrations and waves of all sorts have in commonand includes examples of mechanical, acoustical, and optical manifestations of these phenomena thatunite various parts of physics.

Failure to find an obvious or linear relationship between a developmental experiential factor and a developmental outcome often leads investigators to posit concepts such as “biological preparedness” and “evolved predispositions” that allude to hypothetical geneticmechanisms that may not exist. However, experiential nonlinearities alone may explain the development of certain instinctive behaviors, as shown by studies on alarm call responsivity in mallard ducklings.

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final (...) formulation of Quantum Gravity. (shrink)