入れ子構造型粒子群最適化を用いた非線形力学系のNeimark-Sacker分岐点導出法について

カテゴリ: 論文誌(論文単位)

グループ名: 【C】電子・情報・システム部門

発行日: 2022/06/01

タイトル(英語): Neimark-Sacker Bifurcation Points Derivation Method in Nonlinear Dynamical Systems using Nested-Layer Particle Swarm Optimizations

著者名: 後藤　友綺（中京大学工学部），黒川　弘章（東京工科大学工学部），松下　春奈（香川大学創造工学部），高坂　拓司（中京大学工学部）

著者名(英語): Tomoki Gotoh (Faculty of Engineering, Chukyo University), Hiroaki Kurokawa (Faculty of Engineering, Tokyo University of Technology), Haruna Matsushita (Department of Creative Engineering, Kagawa University), Takuji Kousaka (Faculty of Engineering, Chukyo University)

キーワード: 粒子群最適化(PSO)，Neimark-Sacker分岐，分岐点導出，離散力学系，非自律系　　Particle Swarm Optimizations (PSO)，Neimark-Sacker bifurcation，bifurcation point derivation，discrete dynamical systems，non-autonomous systems

要約(英語): This paper investigates the Neimark-Sacker bifurcation points derivation method using the nested-layer particle swarm optimization (NLPSO) in nonlinear dynamical systems. In nonlinear dynamical systems, Neimark-Sacker bifurcation occurs when a complex conjugate characteristic multiplier crosses the unit circle by changing the parameters. NLPSO is not only under no careful initial values and complex hand calculation but also the advantage of deriving bifurcation points regardless of the stability of the systems. In order to obtain the Neimark-Sacker bifurcation parameters by NLPSO, the characteristic multiplier of the objective function must be set to a complex number. This method derives the local bifurcation points such as Neimark-Sacker bifurcation, period-doubling bifurcation, and saddle-node bifurcation by changing only the declination of the characteristic multiplier without changing the objective function and algorithm. As an application example, we give the results of deriving Neimark-Sacker bifurcation points in two-dimensional discrete dynamical and non-autonomous systems.

本誌: 電気学会論文誌C（電子・情報・システム部門誌） Vol.142 No.6 （2022）

本誌掲載ページ: 670-678 p

原稿種別: 論文／日本語

電子版へのリンク: https://www.jstage.jst.go.jp/article/ieejeiss/142/6/142_670/_article/-char/ja/