Occurrence of Chaos in Higher-Dimensional Discrete-Time Systems

In this paper, the occurrence of chaos is considered in two types of Lotka–Volterra systems: one is the higher-dimensional version of the logistic type system: $x(n + 1) = ax(n)\{ 1 - x(n)\} $, and the other is the higher-dimensional version of the exponential type system: $x(n + 1) = x(n)\exp [ a\{ 1 - x(n)\} ]$. Some simple methods of detecting chaos are presented in these systems. By means of these systems, two classes of examples of the higher-dimensional Benhabib–Day model with chaotic consumer behavior are presented.

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