Bifurcation analysis by particle swarm optimization

Abstract

This paper explains a bifurcation parameter detection strategy based on particle swarm optimization (PSO), and it shows application examples on detection of local bifurcation parameters appearing in discrete-time dynamical systems and non-autonomous continuous dynamical systems. The algorithm design and analysis part shows that the PSO-based algorithm is fairly simple, easily understandable, and easily implementable. The method requires no careful initialization, exact calculation, gradient information of the system, or Lyapunov exponents. However, the simulation results show that the method accurately detects the local bifurcation parameters regardless of the stability of the periodic point.