Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

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Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor. / Kuznetsov, N. V.; Mokaev, T. N.; Vasilyev, P. A.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 19, No. 4, 04.2014, p. 1027-1034.

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

Author

Kuznetsov, N. V. ; Mokaev, T. N. ; Vasilyev, P. A. / Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor. In: Communications in Nonlinear Science and Numerical Simulation. 2014 ; Vol. 19, No. 4. pp. 1027-1034.

BibTeX

@article{0760a8b19c984c2ba902cd0efa5fc91f,

title = "Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor",

abstract = "Exact Lyapunov dimension of attractors of many classical chaotic systems (such as Lorenz, Henon, and Chirikov systems) is obtained. While exact Lyapunov dimension for R{\"o}ssler system is not known, Leonov formulated the following conjecture: Lyapunov dimension of R{\"o}ssler attractor is equal to local Lyapunov dimension in one of its stationary points. In the present work Leonov's conjecture on Lyapunov dimension of various R{\"o}ssler systems with standard parameters is checked numerically.",

keywords = "Chaos, Leonov's conjecture, Lyapunov dimension, Lyapunov exponent, R{\"o}ssler system, Strange attractor",

author = "Kuznetsov, {N. V.} and Mokaev, {T. N.} and Vasilyev, {P. A.}",

note = "Funding Information: This work was supported by the Academy of Finland, Russian Ministry of Education and Science (Federal target programm), Russian Foundation for Basic Research and Saint-Petersburg State University. ",

year = "2014",

month = apr,

doi = "10.1016/j.cnsns.2013.07.026",

language = "English",

volume = "19",

pages = "1027--1034",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier",

number = "4",

}

RIS

TY - JOUR

T1 - Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

AU - Kuznetsov, N. V.

AU - Mokaev, T. N.

AU - Vasilyev, P. A.

N1 - Funding Information: This work was supported by the Academy of Finland, Russian Ministry of Education and Science (Federal target programm), Russian Foundation for Basic Research and Saint-Petersburg State University.

PY - 2014/4

Y1 - 2014/4

N2 - Exact Lyapunov dimension of attractors of many classical chaotic systems (such as Lorenz, Henon, and Chirikov systems) is obtained. While exact Lyapunov dimension for Rössler system is not known, Leonov formulated the following conjecture: Lyapunov dimension of Rössler attractor is equal to local Lyapunov dimension in one of its stationary points. In the present work Leonov's conjecture on Lyapunov dimension of various Rössler systems with standard parameters is checked numerically.

AB - Exact Lyapunov dimension of attractors of many classical chaotic systems (such as Lorenz, Henon, and Chirikov systems) is obtained. While exact Lyapunov dimension for Rössler system is not known, Leonov formulated the following conjecture: Lyapunov dimension of Rössler attractor is equal to local Lyapunov dimension in one of its stationary points. In the present work Leonov's conjecture on Lyapunov dimension of various Rössler systems with standard parameters is checked numerically.

KW - Chaos

KW - Leonov's conjecture

KW - Lyapunov dimension

KW - Lyapunov exponent

KW - Rössler system

KW - Strange attractor

UR - http://www.scopus.com/inward/record.url?scp=84886303693&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2013.07.026

DO - 10.1016/j.cnsns.2013.07.026

M3 - Article

VL - 19

SP - 1027

EP - 1034

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 4

ER -

ID: 7031535