Qualitative Analysis Of Nonlinear Functional Differential With Application

The main aim of this paper is to study the qualitative analysis of nonlinear functional differential with application.In chapter 2, the authors study a class of neural networks, which includes the delayed cellular neural networks and delayed Hopneld neural networks as.its special cases. Some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium are established by means of the Leray-Schauder principle, arithmetic-mean-geometric-mean inequality and new Liapunov functionals.In chapter 3, we study the exponential stability of Lotka-Volterra equation with delay. Sufficient conditions are obtained for the existence and exponential stability of the equilibrium. Sufficient conditions are obtained for the persistence of positive solutions in some periodic integrodifferential systems with feedback controls. We use Horn fixed theory to obtain the existence of a positive periodic solution.In chapter 4, the existence and stability of a periodic solution of Cohen-Grossberg neural networks with multiple delays is investigated, and some sufficient conditions are established to ensure the existence and the global stability of the periodic solution of the network. For the networks with constant input, a unique equilibrium point exists and all other solutions of the network converge to it under the same conditions. Moreover, we study the existence of periodic solution for a class of Cohen-Grossberg neural networks (CGNN) with variable coefficients. By constructing a new Liapunov functional- and using extendable Barbalat theorem, the problem of the global asymptotic stability (GAS) of its periodic solutions is discussed for CGNN.