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Zbl 1094.35128
Song, Qiankun; Cao, Jinde; Zhao, Zhenjiang
Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays. (English)
[J] Nonlinear Anal., Real World Appl. 7, No. 1, 65-80 (2006). ISSN 1468-1218

Summary: Both exponential stability and periodic oscillatory solutions are considered for reaction-diffusion recurrent neural networks with continuously distributed delays. By constructing suitable Lyapunov functional, using $M$-matrix theory and some analysis techniques, some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions for reaction-diffusion recurrent neural networks with continuously distributed delays. Moreover, the exponential convergence rate is estimated. These results have leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for reaction-diffusion recurrent neural networks with continuously distributed delays. Two examples are given to illustrate the correctness of the obtained results.

MSC 2000:: *35Q80 Appl. of PDE in areas other than physics
92B20 General theory of neural networks
35K57 Reaction-diffusion equations
35B35 Stability of solutions of PDE

Keywords: Recurrent neural networks; Reaction-diffusion; Distributed delays; Global exponential stability; Periodic oscillatory solutions; Lyapunov functional; Periodic oscillatory neural circuits

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