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Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays. (English) Zbl 1168.34042
Summary: 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 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.
MSC:
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
34K45Functional-differential equations with impulses
92B20General theory of neural networks (mathematical biology)