Period Doubling Bifurcation Point Detection Strategy with Nested Layer Particle Swarm Optimization

Abstract

This paper proposes a bifurcation point detection strategy based on nested layer particle swarm optimization (NLPSO). The NLPSO is performed by two particle swarm optimization (PSO) algorithms with a nesting structure. The proposed method is tested in detection experiments of period doubling bifurcation points in discrete-time dynamical systems. The proposed method directly detects the parameters of period doubling bifurcation regardless of the stability of the periodic point, but require no careful initialization, exact calculation or Lyapunov exponents. Moreover, the proposed method is an effective detection technique in terms of accuracy, robustness usability, and convergence speed.