Chaos control based on stability Transformation method for unstable periodic orbits

概要

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Stability transformation method has been proposed in order to detect the location of a unstable periodic orbit in a dynamical system which exhibits chaotic behavior. A chaos control approach based on the method has been also considered. The chaos control method can stabilize unknown steady states, however the control method uses <I>l</I>-times iterated Poincaré map corresponding to a periodic orbit of length <I>l</I>. Therefore there is a disadvantage related to robustness and more detailed discussion for realization of the control method is needed. In this paper, we propose a novel chaos control method based on stability transformation method for unstable periodic orbits. The method can stabilize unstable periodic orbits whose states are unknown. We show that our method has a much wider range of control parameters to guarantee stability than ones of a previous method and can be realized by a simple circuit implementation. Some examples are provided and the some theoretical results are confirmed by laboratory measurements.