Global Stability Of Complex-valued Recurrent Neural Networks

Since cellular neural networks were introduced by Chua and Yang in 1988,they were successfully applied,and became a popular research topic in the filed of application mathematics.However,for complex-valued neural networks,up until now,study works are very few.The global exponential stability for a class of complex-valued recurrent neural networks with both asynchronous time-varying delays and impulse is concerned in this paper.Based on the new criterion,we can guarantee the existence,uniqueness,global asymptotical stability and global exponential stability for the equilibrium point of the complex-valued recurrent neural networks if the impulsive effects are not considered in this paper.The main contents in this paper can be summarized as follows:The section 1 is introduction,in which we introduce research background,purpose and significance of complex-valued neural networks,and then give the research status and results of complex-valued neural networks.Finally,the organization of this paper is also presented.In section 2,a class of complex-valued Cohen–Grossberg neural networks with both time delays and impulsive effect are investigated.Some sufficient conditions have been obtained to ensure that complex-valued neural networks have only one equilibrium point and this solution of the system converge to the global exponential stability by the using Lyapunov-Krasovskii functional method and applying algebraic graph theory.Finally,an example with numerical simulation is given to demonstrate the effectiveness of the obtained results.In section 3,we study convergence behaviors of complex-valued cellular neural networks with mixed time delays and impulses.Some sufficient conditions are derived to ensure equilibrium point of complex-valued neural networkswhich converges to zero.by applying mathematical analysis techniques and the properties of inequalities.Finally,some examples showing the effectiveness of the provided criterion are givenIn section 4,the stability of complex-valued delay neural networks with mixed time delays and impulses is investigated.Some sufficient conditions are given to guarantee exponential stability of complex-valued neural networksvia using Lyapunov-Krasovskii functions,linear matrix inequalities(LMIs)and algebraic graph theory.Finally,several examples with numerical simulation are given to demonstrate the effectiveness of the obtained results.