Exact and memory-dependent decay rates to the non-hyperbolic equilibrium of differential equations with unbounded delay and maximum functional

Abstract

In this paper, we obtain the exact rates of decay to the non-hyperbolic equilibrium of the solution of a functional differential equation with maxima and unbounded delay. We study the convergence rates for both locally and globally stable solutions. We also give examples showing how the rate of growth of decay of solutions depends on the rate of growth of the unbounded delay as well as the nonlinearity local to the equilibrium.

Keywords

• functional differential equation
• unbounded delay
• asymptotic stability
• halanay’s inequality
• equations with maxima