Phase Reduction of Stochastic Limit Cycle Oscillators
نویسندگان
چکیده
منابع مشابه
Phase reduction method for strongly perturbed limit cycle oscillators.
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also applicable to strongly perturbed limit cycle oscillators. The fundamental assumption of our method is that the perturbations can be decomposed into a slowly vary...
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We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit cycle. The equation naturally includes previously proposed and mutually exclusive phase equations as special cases. The validity of the theory is numerically con...
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Article history: Received 6 November 2009 Received in revised form 14 February 2010 Accepted 15 February 2010 Available online 19 February 2010 Communicated by C.R. Doering
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We consider optimization of phase response curves for stochastic synchronization of noninteracting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronizatio...
متن کاملSmall noise and long time phase diffusion in stochastic limit cycle oscillators
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise – that is, we modulate the noise by a factor ε ց 0 – and on a long time horizon. We prove explicit estimates on the proximity of the noisy trajectory and the limit cycle up to times...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2008
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.101.154101