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Convergence dynamics of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays
Authors:Yan Lv  Wei Lv  Jianhua Sun  
Institution:aDepartment of Statistics and Financial Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China;bDepartment of Mathematics, Xi’an Jiao Tong University, Xi’an 710049, China;cDepartment of Mathematics, Nanjing University, Nanjing 210093, China
Abstract:Convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov functional method, M-matrix properties, some inequality technique and nonnegative semimartingale convergence theorem are used in our approach. These criteria ensuring the different exponential stability show that diffusion and delays are harmless, but random fluctuations are important, in the stochastic continuously distributed delayed reaction–diffusion RNNs with the structure satisfying the criteria. Two examples are also given to demonstrate our results.
Keywords:Stochastic recurrent neural networks  Reaction–  diffusion  Continuously distributed delay  Exponential stability  Lyapunov functional  Martingale convergence theorem
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