Stable Attracting Sets in Delay Differential Equations and in Their Runge–Kutta Discretizations

Abstract

We show that for sufficiently small step sizes, a Runge–Kutta discretization of an autonomous delay differential equation with a uniformly asymptotically stable compact attracting set of arbitrary shape possesses an attracting set located close to that of the original system.

Keywords:

• Delay differential equations
• Lyapunov functions
• Runge–Kutta methods

AMS Subject Classification:

• 65L05
• 65Q05