Computational Method of Border-collision Bifurcation Point for Piecewise Nonlinear Discrete-Time Dynamical Systems

Abstract

In this paper, we propose a computational method of border-collision bifurcation point for piecewise nonlinear discrete-time dynamical systems. First, an n-dimensional piecewise nonlinear discrete-time dynamical system is defined. Next, we show the conditional equation of border-collision bifurcation and propose the derivation method of the bifurcation points in specific terms. Finally, we confirm the validity of the method by applying it to a two-dimensional piecewise nonlinear discrete-time dynamical system.