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Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays. (English) Zbl 1194.35221
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.

35K57Reaction-diffusion equations
35R10Partial functional-differential equations
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35B10Periodic solutions of PDE
82C32Neural nets (statistical mechanics)
Full Text: DOI
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