2021年4月
Locating and stabilizing unstable periodic orbits embedded in the horseshoe map
International Journal of Bifurcation and Chaos
- ,
- ,
- ,
- 巻
- Vol.31
- 号
- No.4
- 開始ページ
- 2150110
- 終了ページ
- 2150110
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1142/S0218127421501108
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.
- リンク情報
- ID情報
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- DOI : 10.1142/S0218127421501108
- ISSN : 0218-1274