Prerecorded history of a system as an experimental tool to control chaos
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsPublished 1 July 1994
A. Kittel, K. Pyragas, R. Richter
Citations58
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TL;DR
A small self-controlling feedback perturbation transforms an unpredictable chaotic behavior into a predictable chaotic or periodic motion via stabilization of unstable, aperiodic, or periodic orbits of the strange attractor.
Abstract
We present experimental results of synchronizing the current state of a chaotic system with its prerecorded history. This is achieved by a small self-controlling feedback perturbation in the form of the difference between the current state of the system and its past dynamics. The perturbation transforms an unpredictable chaotic behavior into a predictable chaotic or periodic motion via stabilization of unstable, aperiodic, or periodic orbits of the strange attractor. One advantage of the method is its robustness against noise. Furthermore, it does not require any analytical knowledge of the system dynamics and can be simply implemented in experiment by a purely analog technique. The experimental results are supported by a numerical analysis of the conditional Lyapunov exponents and other characteristics of the model equations.
Keywords
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