Horseshoe and topological entropy estimate of a class of three-dimensional cellular neural networks

Abstract

Chaos in a class of three-dimensional continuous time cellular neural networks is investigated. Numerical experiments show that this class of cellular neural networks can display chaotic attractors and limit cycles for different parameters. By virtue of topological horseshoes theory in dynamical systems, a rigorous computer-assisted verification for chaotic behavior of the neural network is presented for certain parameter. Topological entropy estimate of the neural network is also given in terms of the Poincaré map.