Chaos of a new class of Hopfield neural networks

Chaos and bifurcation of a new class of three-dimension Hopfield neural networks are investigated. Numerical experiments show that this class of Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, a numerical bifurcation analysis with plots is given as well. By virtue of horseshoes theory in dynamical systems, we give rigorous computer-assisted verifications for chaotic behavior of the system for certain parameters. Quantitative descriptions of the complexity of these neural networks are also given in terms of topological entropy, and a brief robustness analysis of this class of Hopfield neural networks is also presented.