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Horseshoe chaos in a class of simple Hopfield neural networks. (English) Zbl 1197.37050

Summary: A class of new simple Hopfield neural networks is revisited. To confirm the chaotic behavior in these Hopfield neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
37D45Strange attractors, chaotic dynamics
34C28Complex behavior, chaotic systems (ODE)
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)