title: Complex dynamics in simple Hopfield neural networks.
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.
authors.affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China. yangxs@cqupt.edu.cn
authors.forename: Xiao-Song
authors.initials: XS
authors.lastname: Yang
authors.forename: Yan
authors.initials: Y
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D019277:Entropy; D006358:Hot Temperature; D008433:Mathematics; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods