Existence And Stability Of Solutions For Shunting Inhibitory Cellular Neural Networks

In the paper?we mainly consider the model of shunting inhibitory cellular neural network system with neutral type proportional delays and D operators.and the model of shunting inhibitory cellular neural network system without sat-isfying Lipschitz condition.By using the fixed point theorem and the Lyapunov functional methods,sufficient conditions about the existence and stability of anti-periodic solutions are achieved.This thesis is composed of three chaptersIn Chapter 1,we introduce the historical background,current situation of this article and the main works of this paperIn Chapter 2,we discuss the existence and stability of shunting inhibitory cellular neural network system with neutral type proportional delays and D op-erators.In the existing papers,the passive decay rate of cell and the activation function are strongly restricted.In this paper,the condition of the original model is weakened.First,converting neutral equations into non-neutral equations by constructing operator equations.Second,using the fixed point theorem and the relative differential inequality to obtain the sufficient conditions for the existence and exponential stability of T-anti-periodic solutions,which improves the conclu-sions of the existing studies.Finally,a illustrative example is given to prove the availability of the obtained resultsIn Chapter 3,we discuss the existence and stability of shunting inhibitory cellular neural network system without satisfying Lipschitz condition.A number of studies are based on the global Lipschitz condition.In this paper,we discuss the signal function without satisfying the global Lipschitz condition,by constructing the appropriate Lyapunov function and using the fixed point theorem,we obtain the sufficient conditions for the existence and exponential stability of the anti-periodic solution,which generalizes the results of the existing studies.Finally,a illustrative example is given to prove the availability of the obtained results.