Abstract

The dynamics of ancient civilisations according to credited historians can be explained by means of a simple linear time-invariant feedback model whose loop only consists of a first-order process and a pure time delay. It is shown that, despite its simplicity, this model can give rise to a variety of responses, either oscillatory or aperiodic, such as those envisaged by A. Toynbee. Since modern civilisations are characterised by fast parameter variations, their description calls instead for a time-variant model. Simulations with the linear parameter-varying model obtained from the aforementioned LTI model by letting its parameter vary are carried out to show the influence of different scenarios on the system response. Even if this model is elementary, it is believed that it may serve as a stimulating “tool for thought” in the ever-popular debate on the growth and decline of civilisations.