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

Research output: Contribution to journalArticlepeer-review

83 Scopus citations

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.

Original languageEnglish
Pages (from-to)267-285
Number of pages19
JournalNonlinear Dynamics
Volume92
Issue number2
DOIs
StatePublished - 1 Apr 2018

Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Keywords

  • Adaptive algorithm for the computation of finite-time Lyapunov dimension
  • Finite-time Lyapunov exponents
  • Hidden attractors
  • Perpetual points

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