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Zbl 1194.35221
Zhao, Hongyong; Wang, Guanglan
Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays. (English)
[J] Phys. Lett., A 343, No. 5, 372-383 (2005). ISSN 0375-9601

Summary: We study a class of reaction-diffusion cellular neural networks with delays by introducing ingeniously real parameters $\xi^*_j, \eta _j^*, \alpha ^* _j, \beta ^* _j, \xi _j, \eta_j, \alpha_j, \beta _j$ with $\xi_j^*+\alpha ^*_j = 1$, $\eta_j^*+\beta ^*_j = 1$, $\xi_j+\alpha _j = 1$, $\eta_j+\beta _j = 1$ $(j=1,\ldots, n) $, employing suitable Lyapunov functionals and applying some inequality techniques, we obtain a set of sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic oscillatory solution. These conditions have important leading significance in the design and applications of periodic oscillatory reaction-diffusion neural circuits.

MSC 2000:: *35K57 Reaction-diffusion equations
35R10 Difference-partial differential equations
35B05 General behavior of solutions of PDE
35B10 Periodic solutions of PDE
82C32 Neural nets

Keywords: periodic oscillatory solutions; cellular neural networks; reaction-diffusion; Lyapunov functional

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