Finite-Time And Fixed-Time Synchronization For A Class Of Delayed Cohen-Grossberg Neural Networks

In this paper,we consider the finite time and fixed time synchronization problem for a class of Cohen-Grossberg neural networks with time delays.Based on the drive-response system model,a new control strategy is proposed in this paper,which only depends on the current state of the system,but has nothing to do with the time delay and the delay state of the system.Through rigorous analysis,it can be proved that such time-delay systems can achieve finite-time synchronization or fixed-time synchronization under certain conditions.In fact,in the case of bounded delay,we first classify the initial errors of the system.When the absolute values of each component of this error are large,it can be proved that it will converge to 1 in a finite time.When the absolute value of each component of the error is less than or equal to 1,it can be proved that it will converge to 0 in a fixed time,and the finite-time synchronization or fixed-time synchronization of this kind of drive-response system with bounded time delay is obtained.On the other hand,in the case of large or even unbounded time delay,we improve and extend this method,and it can also be proved that the system can achieve finite-time synchronization or fixed-time synchronization under this control strategy.As a special case,some conclusions about the Hopfiled neural network can also be obtained.Numerical simulation can verify our results well.The overall structure of the article is divided into five chapters:In chapter 1,it introduces the research status of neural network synchronization,the content of this paper and the main innovation points.In chapter 2,we discuss the synchronization of Cohen-Grossberg neural networks with bounded time delays.If the absolute value of each component of the initial state of the systematic error is greater than 1,then we can prove that it will reach 1 in a finite time;If the absolute value of each component in the initial state of the system error is less than or equal to 1,then it will converge to 0 in a fixed time.Taken together,it can be concluded that for any initial value,the system will reach either finite-time synchronization or fixed-time synchronization.In chapter 3,we introduce the finite time and fixed time synchronization problem of Cohen-Grossberg neural networks with unbounded time delay.In chapter 4,it verifies the validity of the conclusion by numerical simulation.In chapter 5,it summarizes the article.