On the periodicity of an implicit difference equation with discontinuity: Analysis and simulations

Abstract

In this note we analyze the periodicity of an implicit nonlinear difference equation subject to perturbations and discontinuity. We prove the existence of multiple periodic solutions under certain conditions, and derive the periods which are functions of the sampling period and the period of the perturbation. In this work, we further present a simulation algorithm which enables the computation of the solution for the implicit difference equation in an iterative manner. The Van der Pol circuit is used as an illustrative example. © World Scientific Publishing Company.