Co-existing hidden attractors in a radio-physical oscillator system

The term 'hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibr...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2015-03, Vol.48 (12), p.125101-12
Main Authors: Kuznetsov, A P, Kuznetsov, S P, Mosekilde, E, Stankevich, N V
Format: Article
Language:English
Subjects:
absence of an equilibrium state
Attraction
Basins
Chaos theory
coexisting chaotic states
Dynamical systems
Dynamics
Functions (mathematics)
hidden attractors
Mathematical analysis
Oscillators
radio-physical oscillator
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Summary:The term 'hidden attractor' relates to a stable periodic, quasiperiodic or chaotic state whose basin of attraction does not overlap with the neighborhood of an unstable equilibrium point. Considering a three-dimensional oscillator system that does not allow for the existence of an equilibrium point, this paper describes the formation of several different coexisting sets of hidden attractors, including the simultaneous presence of a pair of coinciding quasiperiodic attractors and of two mutually symmetric chaotic attractors. We follow the dynamics of the system as a function of the basic oscillator frequency, describe the bifurcations through which hidden attractors of different type arise and disappear, and illustrate the form of the basins of attraction.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/12/125101