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Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses. (English) Zbl 1205.34017
Summary: We present a general class of BAM neural networks with discontinuous neuron activations and impulses. By using the fixed point theorem in differential inclusions theory, we investigate the existence of periodic solution for this neural network. By constructing the suitable Lyapunov function, we give a sufficient condition which ensures the uniqueness and global exponential stability of the periodic solution. The results of this paper show that the Forti’s conjecture is true for BAM neural networks with discontinuous neuron activations and impulses. Further, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.
MSC:
34A60Differential inclusions
34D20Stability of ODE
92B20General theory of neural networks (mathematical biology)
34A37Differential equations with impulses
34C25Periodic solutions of ODE
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