Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays

Authors:
Jie Zhang;Zhanji Gui
Affiliations:
Department of Mathematics, Hainan Normal University, Haikou, Hainan, 571158, PR China;Department of Mathematics, Hainan Normal University, Haikou, Hainan, 571158, PR China and Department of Computer Science, Hainan Normal University, Haikou, Hainan, 571158, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor.