Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich-Fabrikant System

Marius-F Danca, Paul Bourke, Nikolay Kuznetsov

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5 Citations (Scopus)


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 real-time 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.

Original languageEnglish
Article number1930001
Number of pages13
JournalInternational Journal of Bifurcation and Chaos
Issue number1
Publication statusPublished - Jan 2019

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