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Periodic solutions and its exponential stability of reaction-diffusion recurrent neural networks with continuously distributed delays. (English) Zbl 1094.35128
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:
 35Q80 Appl. of PDE in areas other than physics (MSC2000) 92B20 General theory of neural networks (mathematical biology) 35K57 Reaction-diffusion equations 35B35 Stability of solutions of PDE