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arXiv · 1504.04723

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

N. V. Kuznetsov·G. A. Leonov·T. N. Mokaev·A. Prasad·M. D. Shrimali
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Abstract

The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a {hidden attractor} in the case of multistability as well as a classical {self-excited attractor}. The hidden attractor in this system can be localized by analytical-numerical methods based on the {continuation} and {perpetual points}. For numerical study of the attractors' dimension the concept of {finite-time Lyapunov dimension} is developed. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of {exact Lyapunov dimension} are discussed. A comparative survey on the computation of the finite-time Lyapunov exponents by different algorithms is presented and an approach for a reliable numerical estimation of the finite-time Lyapunov dimension is suggested. Various estimates of the finite-time Lyapunov dimension for the hidden attractor and hidden transient chaotic set in the case of multistability are given.

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N. V. Kuznetsov, G. A. Leonov, T. N. Mokaev, A. Prasad, M. D. Shrimali. 2017-11-15. Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system. https://doi.org/10.1007/s11071-018-4054-z

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