Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Issue on Recent Progress in Nonlinear Theory and Its Applications
Bifurcation analysis by particle swarm optimization
Haruna MatsushitaHiroaki KurokawaTakuji Kousaka
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2020 Volume 11 Issue 4 Pages 391-408


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.

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