scholarly journals Looking More Closely at the Rabinovich–Fabrikant System

2016 ◽  
Vol 26 (02) ◽  
pp. 1650038 ◽  
Author(s):  
Marius-F. Danca ◽  
Michal Fec̆kan ◽  
Nikolay Kuznetsov ◽  
Guanrong Chen
Keyword(s):  
Numerical Analysis ◽  
Heteroclinic Orbits ◽  
Transient Chaos ◽  
Hidden Attractors ◽  
Cycling Chaos

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.

scholarly journals Emergence of Hidden Attractors through the Rupture of Heteroclinic-Like Orbits of Switched Systems with Self-Excited Attractors

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
R. J. Escalante-González ◽  
Eric Campos
Keyword(s):  
Switched Systems ◽  
Piecewise Linear ◽  
The Self ◽  
Heteroclinic Orbits ◽  
Bistable System ◽  
Necessary Condition ◽  
Hidden Attractor ◽  
Hidden Attractors

This work is dedicated to the study of an approach that allows the generation of hidden attractors based on a class of piecewise-linear (PWL) systems. The systems produced with the approach present the coexistence of self-excited attractors and hidden attractors such that hidden attractors surround the self-excited attractors. The first part of the approach consists of the generation of self-excited attractors based on pairs of equilibria with heteroclinic orbits. Then, additional equilibria are added to the system to obtain a bistable system with a second self-excited attractor with the same characteristics. It is conjectured that a necessary condition for the existence of the hidden attractor in this class of systems is the rupture of the trajectories that resemble heteroclinic orbits that join the two regions of space that surround the pairs of equilibria; these regions resemble equilibria when seen on a larger scale. With the appearance of a hidden attractor, the system presents a multistable behavior with hidden and self-excited attractors.

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