Looking more closely to the Rabinovich-Fabrikant system
Marius-F. Danca, Michal Feckan, Nikolay Kuznetsov, Guanrong Chen
TL;DR
This paper provides an in-depth numerical analysis of the Rabinovich-Fabrikant system, revealing new chaotic behaviors, hidden attractors, and saddle-like structures, advancing understanding of its complex dynamics.
Contribution
It introduces new characteristics of the Rabinovich-Fabrikant system, including cycling chaos, transient chaos, and hidden attractors, supported by extensive numerical analysis and heteroclinic orbit approximations.
Findings
Discovery of cycling chaos and transient chaos.
Identification of hidden attractors.
Approximate heteroclinic orbits provided.
Abstract
Recently, we look more closely into the Rabinovich-Fabrikant system, after a decade of the study in [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddles-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.
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Taxonomy
TopicsChaos control and synchronization · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems