Exact and Discretized Dissipativity of the Pantograph Equation

Abstract

The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form $x'(t)=g(x(t),x(qt)) (q\in (0,1),t›0)$ is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved that the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.