Search results for "Rabinovich-Fabrikant system"
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Graphical Structure of Attraction Basins of Hidden Chaotic Attractors : The Rabinovich-Fabrikant System
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 o…
Looking More Closely at the Rabinovich-Fabrikant System
2016
Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddle-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.