| Project/Area Number |
16K16124
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Soft computing
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| Research Institution | Kagawa University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 分岐点導出 / 分岐解析 / 初期値設定問題 / 力学系 / 粒子群最適化（PSO） / 進化計算 / 粒子群最適化 / 粒子群最適化(PSO) / 分岐 / 離散力学系 / 不安定周期点 / 非線形解析 / 非線形最適化 / 群知能 / ソフトコンピューティング |
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| Outline of Final Research Achievements |
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 local bifurcation points in discrete-time dynamical systems. The proposed method directly detected the parameters of period doubling bifurcation and saddle-node bifurcation in both discrete-time and continuous dynamical systems, 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.
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| Academic Significance and Societal Importance of the Research Achievements |
分岐解析は，非線形的挙動を取るあらゆる系にとって重要である．これは，数理モデルのみならず，自動車や電気回路，自然現象など実社会の多岐に渡る．提案手法は煩雑な式変形や注意深い初期値設定，厄介なパラメータ設定を必要としないため，従来はノウハウなしには行えなかった分岐解析の簡略化へ貢献するだけでなく，微分不可能なモデルの分岐解析を可能とするのではないかと考える．つまり，多くの現象やパラメータを含んだ高次元数理モデルの開発，およびそれらの詳細な非線形解析が期待できる．これにより，生体や自然現象等様々な分野の精密な理解，制御，予測，発展が期待できる．
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