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

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...

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Bibliographic Details
Published in:Nonlinear dynamics 2018-04, Vol.92 (2), p.267-285
Main Authors: Kuznetsov, N. V., Leonov, G. A., Mokaev, T. N., Prasad, A., Shrimali, M. D.
Format: Article
Language:English
Subjects:
Adaptive algorithms
Automotive Engineering
Chaos theory
Classical Mechanics
Control
Dynamical Systems
Engineering
Liapunov exponents
Mechanical Engineering
Numerical methods
Original Paper
Vibration
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Summary: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. The concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors. 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 and dimension by different algorithms is presented. An adaptive algorithm for studying the dynamics 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.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4054-z