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

TL;DR

This paper determines precise decay rates to non-hyperbolic equilibria in differential equations with unbounded delay, revealing how decay depends on delay growth and nonlinearity.

Contribution

It provides exact decay rates for solutions of functional differential equations with maxima and unbounded delay, including local and global stability analysis.

Findings

Decay rates depend on unbounded delay growth

Exact decay rates are established for non-hyperbolic equilibria

Examples illustrate the influence of nonlinearity and delay on decay

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.