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  • Title: Complex dynamics in simple Hopfield neural networks.
    Author: Yang XS, Huang Y.
    Journal: Chaos; 2006 Sep; 16(3):033114. PubMed ID: 17014219.
    Abstract:
    A class of simple Hopfield neural networks with a parameter is investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated; the bifurcation plot and several important phase portraits are presented as well. By virtue of a recent result of horseshoe theory in dynamical systems, we present rigorous computer-assisted verifications for chaotic behavior in the simple Hopfield neural networks for certain parameters and give a brief discussion on the robustness of the chaotic behavior. Quantitative descriptions of the complexity of these neural networks are also given in terms of topological entropy.
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