Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Issue on Evolutionary Computation
Nested-layer particle swarm optimization method for bifurcation point detection in non-autonomous systems
Haruna MatsushitaWataru KinoshitaHiroaki KurokawaTakuji Kousaka
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2019 Volume 10 Issue 3 Pages 289-302

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Abstract

Nested-layer particle swarm optimization (NLPSO) is a powerful method to detect bifurcation parameters in discrete-time dynamical systems. Although NLPSO requires no carefully set initial system parameters, Lyapunov exponents or derivation of objective functions, the method can quickly and accurately detect the bifurcation parameter. Previous studies have proven the effectiveness of NLPSO for discrete-time dynamical systems, but they have not demonstrated the effectiveness of continuous dynamical systems. This study proposes an NLPSO-based method to detect bifurcation parameters in non-autonomous continuous-time dynamical systems and applies the method to the Duffing equation. By adding Poincaré maps computation to the algorithm, the NLPSO accurately detected period-doubling and saddle-node bifurcation parameters in the non-autonomous dynamical systems and the discrete-time dynamical systems, without a change in objective functions.

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© 2019 The Institute of Electronics, Information and Communication Engineers
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