Mathematica Eterna
Open Access

Abstract

Complex in a Simple Delayed Discrete Neural Network

Yuanlong Chen and Xiaoying Wu

In this paper, we show that a delayed discrete Hopfield neural network of two identical neurons with no self-connections can demonstrate chaotic behavior away from the origin. To this end, we first transform the model, by a novel way, into an equivalent system which enjoys some nice properties, and construct chaotic invariant sets of this system such that the dynamics is conjugate to the shift with two symbols. This is complementary to the results in Huang and Zou (J. Nonlinear Sci.,15(2005), 291-303), where it was shown that the same system can have chaotic behavior near the origin.