TWO KINDS OF HORSESHOES IN A HYPERCHAOTIC NEURAL NETWORK.

This paper studies the hyperchaotic dynamics in a four-dimensional Hopfield neural network by virtue of topological horseshoe. Two different horseshoes (chaotic invariant sets) are found in this network with the same parameters. Numerical studies show that the first one expands only one-dimensionally and the second one expands two-dimensionally. Computer simulation also shows that there exists a heteroclinic connection from the second horseshoe to the first one, which indicates that the chaotic set of this system can have a very complicated structure composed of different kinds of expansions. [ABSTRACT FROM AUTHOR]