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
© 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.
PublisherWorld Scientific Publishing Co. Pte. Ltd.
ISSN Search the Publication Forum0218-1274
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