Periodic and aperiodic consumer behavior (Q1094303)

Various properties of nonlinear difference equations are analyzed within the framework of a model of endogenous preference change. Theorems by Sharkovskij and Li and Yorke show that simple first order nonlinear difference equations exhibit a wide range of dynamical behavior: Stable points, a hierarchy of stable cycles, unstable cycles, and an uncountable set of aperiodic points. The economic analysis in this paper focuses in particular on the sequence of stable cycles and asks questions about rationality and consistent behavior over time within a structure of utility maximization.