CHAOS, BIFURCATION AND ROBUSTNESS OF A CLASS OF HOPFIELD NEURAL NETWORKS

Author:

HUANG WEN-ZHI1,HUANG YAN2

Affiliation:

1. School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan 430073, P. R. China

2. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

Abstract

Chaos, bifurcation and robustness of a new class of Hopfield neural networks are investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, the bifurcation plot and several important phase portraits are presented as well. By virtue of horseshoes theory in dynamical systems, rigorous computer-assisted verifications for chaotic behavior of the system with certain parameters are given, and here also presents a discussion on the robustness of the original system. Besides this, quantitative descriptions of the complexity of these systems are also given, and a robustness analysis of the system is presented too.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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