Chaos on Discrete Neural Network Loops with Self-Feedback

Abstract

In this paper, the complex dynamical behaviors in a discrete neural network loop with self-feedback are studied. Specifically, an invariant closed set of the system of neural network loops is built and the subsystem restricted on this invariant closed set is topologically conjugate to a two-sided symbolic dynamical system which has two symbols. In the end, some illustrative numerical examples are given to demonstrate our theoretical results.

Heteroclinic Cycles Imply Chaos and Are Structurally Stable

“…Since Li and Yorke first introduced the term "chaos" in 1975 [1], chaotic dynamics have been observed in various fields [2][3][4][5][6][7][8][9][10]. When chaotic theory was in its initial stage, Marotto generalized the results of Li and Yorke in interval mapping to multidimensional discrete systems and proved that a snapback repeller implies chaos [11].…”