Global Exponential Stability for Nonlinear Delay Differential Systems

Abstract

We give a review on recent results for global stability for nonlinear functional differential equations. Such equations include delay differential equations, integro-differential equations and equations with distributed delay and are applied as mathematical models in Population Dynamics and other sciences. We also consider methods used to study global stability: constructing of Lyapunov functional, applications of special matrices such as M-matrix or special matrix functions such as matrix measure, method of matrix inequalities, which is very popular in papers on Control Theory, fixed point approach and using a notion of nonlinear Volterra operator.