Particle swarm optimization-based strategy for detecting border-collision bifurcation points in piecewise smooth maps

Abstract

A border-collision bifurcation point detection strategy based on particle swarm optimization (PSO) is proposed in this paper, and it facilitates a bifurcation point detection in piecewise smooth maps. This method is tested via detection experiments of border-collision bifurcation points in two popular piecewise smooth maps with one or more borders. The algorithm design and analysis part shows that the proposed algorithm is fairly simple, easily understandable, and easily implementable. The simulation results show that it accurately detects the border-collision parameters of the target period regardless of its stability, but requires no careful initialization or gradient information of the system.