Harmless Feedback Control for Permanence and Global Asymptotic Stability in Nonlinear Delay Population Equation

Abstract

In this paper, we consider whether or not the feedback control has influence on a nonlinear population equation with several time delays. The general criteria of integrable form on the permanence are established, and we note that the feedback control has no influence to the permanence of system. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global asymptotic stability of any positive solutions to the system.