The Stability Analysis Of Cohen-Grossberg Neural Network With Time-varying Delays

In this paper, we analyze the dynamical behaviors by using Lyapunov functional and matrix inequalities, including the existence, uniqueness, and global exponential stability of the equilibrium point for Cohen-Grossberg neural network with delays and impulses, and the global robust exponential stability of Cohen-Grossberg neural network with time-varying delays.The main work is illustrated as follows:First, without assuming that the activation functions are bounded, employing the homeomorphism theorem and the fixed point theorem, we establish some sufficient conditions for the existence and uniqueness of the equilibrium point of Cohen-Grossberg neural network with delays and impulses.Second, on the base of the existence and uniqueness of the equilibrium point, we present sufficient conditions for the global exponential stability of Cohen-Grossberg neural network with delays and impulses by constructing suitable Lyapunov functional and using the technique of integral inequality. The main results are compared with the previously published results, and it is shown that the obtained results improve and generalize the previously published results. An example is also given to illustrate the effectiveness of our results.Third, constructing Lyapunov functional and using an inequality, we study the robust stability of Cohen-Grossberg neural network with time-varying delays. Some criteria ensuring the existence and the global robust exponential stability of a unique equilibrium point for Cohen-Grossberg neural network with time-varying delays are obtained. Some corollaries and an example are given to show that our results generalize the previously reported results.