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Zbl 1205.34017
Wu, Huaiqin; Shan, Caihong
Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses. (English)
[J] Appl. Math. Modelling 33, No. 6, 2564-2574 (2009). ISSN 0307-904X

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 2000:: *34A60 ODE with multivalued right-hand sides
34D20 Lyapunov stability of ODE
92B20 General theory of neural networks
34A37 Differential equations with impulses
34C25 Periodic solutions of ODE

Keywords: neural networks; global exponential stability; neuron activation functions; impulses; periodic solution; differential inclusions

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