Horseshoe Dynamics in a Small Hyperchaotic Neural Network

This paper studies the hyperchaotic dynamics in a four dimensional Hopfield neural network. A topological horseshoe on a three dimensional block is found in a carefully chosen Poincare section hyperplane of the ordinary differential equations. Numerical studies show that there exist two-directional expansions in this horseshoe map. In this way, a computer-assisted verification of hyperchaoticity of this neural network is presented by virtue of topological horseshoe theory.

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