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Zbl 1197.35144
Lu, Jun Guo; Lu, Lin Ji
Global exponential stability and periodicity of reaction-diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions. (English)
[J] Chaos Solitons Fractals 39, No. 4, 1538-1549 (2009). ISSN 0960-0779

Summary: Global exponential stability and periodicity of a class of reaction-diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions are studied by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential convergence to 0 of the difference between any two solutions of the original neural networks, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Secondly, we prove periodicity. Sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution are given. These conditions are easy to verify and our results play an important role in the design and application of globally exponentially stable neural circuits and periodic oscillatory neural circuits. \par Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC 2000:: *35K57 Reaction-diffusion equations
35B10 Periodic solutions of PDE
35B35 Stability of solutions of PDE
35K51
92B20 General theory of neural networks

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