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Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system. / Kuznetsov, N. V.; Leonov, G. A.; Mokaev, T. N.; Prasad, A.; Shrimali, M. D.

In: Nonlinear Dynamics, Vol. 92, No. 2, 01.04.2018, p. 267-285.

Research output: Contribution to journal › Article › peer-review

Harvard

Kuznetsov, NV, Leonov, GA, Mokaev, TN, Prasad, A & Shrimali, MD 2018, 'Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system', Nonlinear Dynamics, vol. 92, no. 2, pp. 267-285. https://doi.org/10.1007/s11071-018-4054-z

APA

Kuznetsov, N. V., Leonov, G. A., Mokaev, T. N., Prasad, A., & Shrimali, M. D. (2018). Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system. Nonlinear Dynamics, 92(2), 267-285. https://doi.org/10.1007/s11071-018-4054-z

Vancouver

Kuznetsov NV, Leonov GA, Mokaev TN, Prasad A, Shrimali MD. Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system. Nonlinear Dynamics. 2018 Apr 1;92(2):267-285. https://doi.org/10.1007/s11071-018-4054-z

Author

Kuznetsov, N. V. ; Leonov, G. A. ; Mokaev, T. N. ; Prasad, A. ; Shrimali, M. D. / Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system. In: Nonlinear Dynamics. 2018 ; Vol. 92, No. 2. pp. 267-285.

BibTeX

@article{6649a12f9931455a8b7d557fa5725ed2,
title = "Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system",
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. 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.",
keywords = "Adaptive algorithm for the computation of finite-time Lyapunov dimension, Finite-time Lyapunov exponents, Hidden attractors, Perpetual points",
author = "Kuznetsov, {N. V.} and Leonov, {G. A.} and Mokaev, {T. N.} and A. Prasad and Shrimali, {M. D.}",
year = "2018",
month = apr,
day = "1",
doi = "10.1007/s11071-018-4054-z",
language = "English",
volume = "92",
pages = "267--285",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

AU - Kuznetsov, N. V.

AU - Leonov, G. A.

AU - Mokaev, T. N.

AU - Prasad, A.

AU - Shrimali, M. D.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - 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.

AB - 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.

KW - Adaptive algorithm for the computation of finite-time Lyapunov dimension

KW - Finite-time Lyapunov exponents

KW - Hidden attractors

KW - Perpetual points

UR - http://www.scopus.com/inward/record.url?scp=85044536815&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/finitetime-lyapunov-dimension-hidden-attractor-rabinovich-system

U2 - 10.1007/s11071-018-4054-z

DO - 10.1007/s11071-018-4054-z

M3 - Article

AN - SCOPUS:85044536815

VL - 92

SP - 267

EP - 285

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 2

ER -

ID: 35274833