Boundedness, periodic solutions and global stability for cellular neural networks with variable coefficients and infinite delays

In this paper, we consider the cellular neural networks with variable coefficients and infinite distributed delays. By introducing the phase space Cg(R-)Cg(R-) and applying Lyapunov functional method and Young inequality technique, we first establish a series of criteria on the boundedness, globally asymptotic stability and globally exponential stability. Furthermore, by applying these results and combining the existence theorems of periodic solutions for general functional differential equations with infinite delays, we establish the existence of periodic solutions and its globally asymptotic stability and globally exponential stability for the periodic cellular neural networks with infinite distributed delays. At last, as a special case, we apply these results to the autonomous cellular neural networks with infinite distributed delays and the existence, uniqueness and global stability of equilibrium point are established.