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1. Introduction



This work aims to investigate and visualize as clearly as possible the dynamics of the so-called "dynastic cycle" model. The dynastic cycle models a three-class society of farmers, bandits and soldiers and is derived from Chinese history.

According to [Ush89] a dynastic cycle is a periodic alternation of the society between despotism and anarchy. As illustration he mentions the Chinese history: a new line of emperors creates a powerful regime of peace and property, but when the dynasty becomes older, a downswing takes place, which is accompanied by civil war, misery, poverty and population decline.

[FFP93] present a model very similar to the one introduced by [Ush89]. In my further work I want to refer to this second model. As in the first model, [FFP93] also investigate a model of society with three classes, which are the same as in the first system. The three class society consists of farmers who produce some goods, bandits who steal these goods, and of soldiers who try to protect the farmers by fighting the bandits, but also tax the farmers.

When talking about the "dynastic cycle", a periodic alternation between two states of the society is meant. The first state is arnarchy, when an equilibrium develops between bandits who steal and farmers who try to defend their goods, without any public authority. The second one is despotism, when soldiers tax the farmers and fight the bandits in order to protect their incomes from the tax revenue. Therefore soldiers punish bandits by execution.
In the first case (that is in the absence of any public authority) the model of [FFP93] supposes that farmers and bandits interact dynamically, according to a usual predator-prey relationship.

Most of the visualizations were done in the DynSys3D - System, a system that provides many different tools for visualizing analytically defined three-dimensional dynamical systems in the AVS System.

The rest of this work is organized as follows: