Biological populations obeying difference equations : stable points, stable cycles, and chaos.

For biological populations with nonoverlapping generations, population growth takes place in discrete time steps and is described by difference equations.Some of the simplest such nonlinear equations can exhibit a remarkable spectrum of dynamical behaviour, from stable equilibrium points, to stable cyclic oscillations between two population points, to stable cycles with four points, then eight, 16, etc., points, through to a chaotic regime in which cycles of any period, can occur.