徳島大学 教育・研究者情報データベース(EDB)

1. 徳島大学.情報センター(2010年7月1日〜)

1. 美井野 優([鳴門教育大学])

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2. 伊藤 大輔([岐阜大学]/滋賀県立大学)

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3. 上田 哲史([徳島大学.情報センター]/[徳島大学.理工学部.理工学科.知能情報コース.情報工学講座])

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4. 川上 博

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(英) Locating and stabilizing unstable periodic orbits embedded in the horseshoe map

(英) Based on the theory of symbolic dynamical systems, we propose a novel computation method to locate and stabilize the unstable periodic points (UPPs) in a two-dimensional dynamical system with a Smale horseshoe. This method directly implies a new framework for controlling chaos. By introducing the subset based correspondence between a planar dynamical system and a symbolic dynamical system, we locate regions sectioned by stable and unstable manifolds comprehensively and identify the speci ed region containing a UPP with the particular period. Then Newton's method compensates the accurate location of the UPP with this region information as an initial guess. On the other hand, the external force control (EFC) is known as an e ective method to stabilize the UPPs. By applying the EFC to the located UPPs, robust controlling chaos is realized. In this framework, we never use ad hoc approaches to nd target UPPs in the given chaotic set. Moreover, the method can stabilize UPPs with the speci ed period regardless of the situation where the targeted chaotic set is attractive or not. As illustrative numerical experiments, we locate and stabilize UPPs and the corresponding unstable periodic orbits in a horseshoe structure of the Du ng equation. In spite of the strong instability of UPPs, the controlled orbit is robust and the control input retains tiny in magnitude.

1. カオス(chaos)
2. (英) horseshoe map
3. (英) symbolic dynamics
4. (英) unstable periodic point
5. 数値計算(numerical computation)
6. (英) controlling chaos