Graphical Structure of Attraction Basins of Hidden Chaotic Attractors : The Rabinovich-Fabrikant System
Danca, Marius-F., Bourke, P., & Kuznetsov, N. (2019). Graphical Structure of Attraction Basins of Hidden Chaotic Attractors : The Rabinovich-Fabrikant System. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 29(1), Article 1930001. https://doi.org/10.1142/S0218127419300015
Date
2019Copyright
© World Scientific Publishing Company 2019
The attraction basin of hidden attractors does not intersect with small neighborhoods of any equilibrium point. To the best of our knowledge this property has not been explored using realtime interactive three-dimensions graphics. Aided by advanced computer graphic analysis, in this paper, we explore this characteristic of a particular nonlinear system with very rich and unusual dynamics, the Rabinovich–Fabrikant system. It is shown that there exists a neighborhood of one of the unstable equilibria within which the initial conditions do not lead to the considered hidden chaotic attractor, but to one of the stable equilibria or are divergent. The trajectories starting from any neighborhood of the other unstable equilibria are attracted either by the stable equilibria, or are divergent.
Publisher
World Scientific Publishing Co. Pte. Ltd.ISSN Search the Publication Forum
0218-1274Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/28916272
Metadata
Show full item recordCollections
License
Related items
Showing items with similar title or keywords.
-
Localization and dimension estimation of attractors in the Glukhovsky-Dolzhansky system
Mokaev, Timur (University of Jyväskylä, 2016) -
Numerical analysis of dynamical systems : unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension
Kuznetsov, Nikolay; Mokaev, Timur (IOP Publishing, 2019)In this article, on the example of the known low-order dynamical models, namely Lorenz, Rössler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz ... -
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
Danca, Marius-F.; Fečkan, Michal; Kuznetsov, Nikolay; Chen, Guanrong (Springer, 2018) -
Hidden Strange Nonchaotic Attractors
Danca, Marius-F.; Kuznetsov, Nikolay (MDPI AG, 2021)In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the ... -
The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension
Kuznetsov, N. V.; Mokaev, T. N.; Kuznetsova, O. A.; Kudryashova, E. V. (Springer, 2020)On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global ...