On the attractors of two-dimensional Rayleigh oscillators including noise

Abstract

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops several rotational excitations with right/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations.

arXiv comment9 pages, 5 figures

References in corpus (8)

• Novel type of phase transition in a system of self-driven particles
• Social Force Model for Pedestrian Dynamics
• Onset of collective and cohesive motion
• Self-organization in systems of self-propelled particles
• Spontaneously ordered motion of self-propelled particles
• Brownian Particles far from Equilibrium
• Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics
• Active Brownian Particle and Random Walk Theories of the Motions of Zooplankton: Application to Experiments with Swarms of Daphnia

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