イベント名
Distinguished Lecturer Program Series
発表年月日
2023/03/15
タイトル
Locating and Controlling Chaotic Saddles
講演者
上田　哲史(徳島大学), 
抄録
Some planar discrete nonlinear systems may have a horseshoe structure with stable and unstable manifolds associated with a saddle fixed point. Under this situation, as is well known, there are infinitely many unstable periodic points around the saddle. By making correspondence of the cross sections of manifolds and symbolic dynamics, one can obtain a “candidate area” containing an unstable periodic point whose period is given by the gray code. These unstable periodic points can be stabilized by applying any chaos control technique into that candidate area, for which the external force control method exhibits a very robust control performance. In this talk, a horseshoe structure derived by the Poincaré mapping for a two-dimensional nonautonomous hybrid system is analyzed as an example. As an example, locating scheme for unstable periodic points is demonstrated, and their control results are presented.
Some planar discrete nonlinear systems may have a horseshoe structure with stable and unstable manifolds associated with a saddle fixed point. Under this situation, as is well known, there are infinitely many unstable periodic points around the saddle. By making correspondence of the cross sections of manifolds and symbolic dynamics, one can obtain a “candidate area” containing an unstable periodic point whose period is given by the gray code. These unstable periodic points can be stabilized by applying any chaos control technique into that candidate area, for which the external force control method exhibits a very robust control performance. In this talk, a horseshoe structure derived by the Poincaré mapping for a two-dimensional nonautonomous hybrid system is analyzed as an example. As an example, locating scheme for unstable periodic points is demonstrated, and their control results are presented.

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