The Wheel of Fortune
– an allegorical image of the cyclical nature of rise and fall of rulers, nations, empires, and civilizations. One problem with it, however, is that it suggests a too mechanical view of historical dynamics.

Regular cycles is just one of possible behaviors that can arise in nonlinear dynamical systems, and not the most common one. Nonlinear feedbacks between different interacting components often cause dynamical systems to behave in complex ways (mathematical chaos is one such behavior ). Furthermore, in addition to endogenous feedbacks (interactions between its internal parts) dynamical systems may be affected by exogenous influences, which we often model as stochastic factors. Stochastic exogenous factors combine with endogenous feedbacks to produce a great variety of complex dynamical behaviors in real-life dynamical systems, whether physical, biological, or social.