The estimates of Lyapunov dimension in attractors of generalized Rossler systems

Authors

  • Gennadiy A. Leonov St.Petersburg State University, Universitetskiy pr., 28, St.Petersburg, Stariy Petergof, 198504, Russian Federation; National Research University Higher School of Economics, ul. Souza Pechatnikov, 16, St. Petersburg, 190008, Russian Federation
  • Tatyana A. Alexeeva St.Petersburg State University, Universitetskiy pr., 28, St.Petersburg, Stariy Petergof, 198504, Russian Federation; National Research University Higher School of Economics, ul. Souza Pechatnikov, 16, St. Petersburg, 190008, Russian Federation

Abstract

Some generalization of one classical R¨ossler systems are reviewed and efficacy of Lyapunov functions plotting for the estimates of these systems attractors dimensions is demonstrated. The estimates of Lyapunov dimension of attractors for generalized R¨ossler systems are obtained with their help. For the local Lyapunov dimensions of attractors for the indicated systems the accurate formulas are cited. For the extreme occurrence the congruency of topological, Hausdorff, fractal and Lyapunov dimensions of attractors is obtained. It is also demonstrated, that under standard values of R¨ossler parameters, the formules of local Lyapunov dimensions at zero point are congruent with the meanings obtained in numerical experiments. Refs 16. Figs 2.

Keywords:

Lyapunov functions, Rossler system, Lyapunov dimension, attractor

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Published

2014-11-01

How to Cite

Leonov, G. A., & Alexeeva, T. A. (2014). The estimates of Lyapunov dimension in attractors of generalized Rossler systems. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 1(4), 544–550. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11087

Issue

Vol. 1 No. 4 (2014)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.