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Saddle-node bifurcation parameter detection strategy with nested-layer particle swarm optimization

Author

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  • Matsushita, H.
  • Kurokawa, H.
  • Kousaka, T.

Abstract

Nested-layer particle swarm optimization (NLPSO) detects bifurcation parameters in discrete-time dynamical systems. Previous studies have proven the effectiveness of NLPSO for period-doubling bifurcations, but not for other bifurcation phenomena. This paper demonstrates that NLPSO can effectively detect saddle-node bifurcations. Problems in detecting saddle-node bifurcation parameters by conventional NLPSO are clarified, and are solved by imposing a simple condition on the NLPSO objective function. Under this conditional objective function, the NLPSO accurately detected both saddle-node and period-doubling bifurcation parameters regardless of their stability, without requiring careful initialization, exact calculations or Lyapunov exponents.

Suggested Citation

  • Matsushita, H. & Kurokawa, H. & Kousaka, T., 2019. "Saddle-node bifurcation parameter detection strategy with nested-layer particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 126-134.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:126-134
    DOI: 10.1016/j.chaos.2018.12.016
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    References listed on IDEAS

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    1. Liu, Bo & Wang, Ling & Jin, Yi-Hui & Tang, Fang & Huang, De-Xian, 2006. "Directing orbits of chaotic systems by particle swarm optimization," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 454-461.
    2. Gao, Fei & Gao, Hongrui & Li, Zhuoqiu & Tong, Hengqing & Lee, Ju-Jang, 2009. "Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-Lyapunov way," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2450-2463.
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    Cited by:

    1. Matsushita, Haruna & Kurokawa, Hiroaki & Kousaka, Takuji, 2023. "Non-gradient-based simultaneous strategy for bifurcation parameter detection," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Liu, Lianggui & Zhang, Rui & Chen, Qiuxia, 2022. "High-performance global peak tracking technique for PV arrays subject to rapidly changing PSC," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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