6533b81ffe1ef96bd1278fdc

RESEARCH PRODUCT

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

Nikolay KuznetsovNikolay KuznetsovManish Dev ShrimaliAwadhesh PrasadTimur N. MokaevGennady A. Leonov

subject

Lyapunov functionMathematics::Dynamical SystemsChaoticAerospace EngineeringFOS: Physical sciencesOcean EngineeringLyapunov exponent01 natural sciences010305 fluids & plasmasadaptive algorithmssymbols.namesakehidden attractorsDimension (vector space)0103 physical sciencesAttractorApplied mathematicsElectrical and Electronic Engineering010301 acousticsMultistabilityMathematicsAdaptive algorithmApplied MathematicsMechanical EngineeringNumerical analysisNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsControl and Systems EngineeringLyapunov dimensionsymbolsperpetual pointsChaotic Dynamics (nlin.CD)finite-time Lyapunov exponents

description

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.

yearjournalcountryeditionlanguage
2015-04-18
https://dx.doi.org/10.48550/arxiv.1504.04723