Abstract
We present a novel technique for stabilizing unstable periodic orbits of chaotic systems. It uses a continuous feedback loop in the form of the difference between an actual and a delayed output signal of the system with a variable delay time. This time is chosen to be equal to the interval between the last and the k-th previous maximum of the output signal and is changed at every k-th maximum. During the procedure, the delay time asymptotically tends to the period of the period-k unstable periodic orbits and the control signal vanishes. The method is illustrated with the help of the Rössler ordinary differential equations and the Mackey-Glass delay differential equations. Eventually, the experimental realization of the control method is demonstrated.
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© 1996 Springer-Verlag
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Kittel, A., Popp, M., Parisi, J., Pyragas, K. (1996). Control of chaos by self-adapted delayed feedback. In: Parisi, J., Müller, S.C., Zimmermann, W. (eds) Nonlinear Physics of Complex Systems. Lecture Notes in Physics, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105442
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DOI: https://doi.org/10.1007/BFb0105442
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