Noise scaling of phase synchronization of chaos

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 3, 2000, Pages 3230-3233

  Andrade, Victor ^a   Davidchack, Ruslan L ^a   Lai, Ying Cheng ^b  

^a UNIVERSITY OF KANSAS   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CIRCUIT OSCILLATIONS; WHITE NOISE;

ADDITIVE WHITE NOISE; COUPLED CHAOTIC OSCILLATORS; EFFECT OF NOISE; HEURISTIC DERIVATIONS; NOISE AMPLITUDE; PARAMETER REGIMES; PHASE SYNCHRONIZATION; TEMPORAL PHASE;

SYNCHRONIZATION;

EID: 0000472945     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.3230     Document Type: Article

References (19)

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18. A dynamical quantity that characterizes the onset of phase synchronization is the Lyapunov spectrum 2. Under the influence of noise, the spectrum as a function of the coupling parameter is typically shifted by an amount that is proportional to the noise amplitude, so that a larger coupling strength is required for phase synchronization to occur. However, there appears, to be no direct correspondence between the Lyapunov spectrum and the superpersistent transient scaling law.
19. An alternative explanation for noise-induced 2π phase slips in chaotic phase synchronization is as follows. From our potential model, in the regime of phase synchronization (Formula presented) the depths of the potential wells are larger than the maximum amplitude of the chaotic fluctuations. Therefore, in the absence of noise, a particle trapped in one of the potential wells cannot move to the adjacent wells. Under the influence of noise, when the combined amplitude of the noise and chaotic fluctuations exceeds the depth of the potential well, 2π phase slips can occur. This is similar to the case before phase synchronization (Formula presented) where the depth of the potential well is smaller than the amplitude of the chaotic fluctuations. In this sense, intuitively, the phenomenon of noise induced 2π phase slips is similar to that observed before phase synchronization 5. The parameter regime slightly before phase synchronization where the phase slips are rare is called the nearly synchronous regime 2. The contribution of our paper, however, is a quantitative scaling analysis of the effect of noise on phase synchronization, which, to our knowledge, has not been reported before.