0000000000223430

AUTHOR

D. V. Kusakin

showing 3 related works from this author

Estimation of Lyapunov dimension for the Chen and Lu systems

2015

Nowadays various estimates of Lyapunov dimension of Lorenz-like systems attractors are actively developed. Within the frame of this study the question arises whether it is possible to obtain the corresponding estimates of dimension for the Chen and Lu systems using the reduction of them to the generalized Lorenz system. In the work (Chen and Yang, 2013) Leonov's method was applied for the estimation of Lyapunov dimension, and as a consequence the Lyapunov dimension of attractors of the Chen and Lu systems with the classical parameters was estimated. In the present work an inaccuracy in (Chen and Yang, 2013) is corrected and it is shown that the revised domain of parameters, where the estima…

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsFOS: MathematicsFOS: Physical sciencesDynamical Systems (math.DS)Chaotic Dynamics (nlin.CD)Mathematics - Dynamical SystemsNonlinear Sciences - Chaotic Dynamics
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The Lyapunov dimension formula for the global attractor of the Lorenz system

2015

The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the …

Lyapunov functionClass (set theory)Mathematics::Dynamical SystemsKaplan-Yorke dimensionFOS: Physical sciencesLyapunov exponentDynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)010305 fluids & plasmassymbols.namesakeDimension (vector space)Lorenz system0103 physical sciencesAttractorFOS: MathematicsMathematics - Dynamical Systems010301 acousticsMathematicsNumerical AnalysisApplied MathematicsMathematical analysista111Lyapunov exponentsLorenz systemNonlinear Sciences - Chaotic DynamicsNonlinear Sciences::Chaotic DynamicsModeling and SimulationsymbolsLyapunov dimensionself-excited Lorenz attractorVariety (universal algebra)Chaotic Dynamics (nlin.CD)
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Lyapunov dimension formula for the global attractor of the Lorenz system

2016

The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique of special Lyapunov-type functions, which was developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters, of the system, such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which sati…

Nonlinear Sciences::Chaotic DynamicsLorenz systemLyapunov dimensionLyapunov exponentsself-excited Lorenz attractorKaplan-Yorke dimension
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