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Zbl 1134.35066
Lu, Jun Guo
Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. (English)
[J] Chaos Solitons Fractals 35, No. 1, 116-125 (2008). ISSN 0960-0779

Summary: The global exponential stability and periodicity for a class of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are addressed by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential converge to zero of the difference between any two solutions of the original reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, the existence and uniqueness of equilibrium is the direct result 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. Furthermore, we prove periodicity of the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Sufficient conditions ensuring the global exponential stability and the existence of periodic oscillatory solutions are given. These conditions are easy to check and have important leading significance in the design and application. Finally, two numerical examples are given to show the effectiveness of the obtained results.

MSC 2000:: *35K57 Reaction-diffusion equations
35B35 Stability of solutions of PDE
35R10 Difference-partial differential equations
92B20 General theory of neural networks

Keywords: Lyapunov functionals

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Zentralblatt MATH Berlin [Germany]