Non-equilibrium of a general stochastic system of coupled oscillators: entropy production rate and rotation numbers

Abstract

Link to this article: http://journals.cambridge.org/abstract_S0143385705000064How to cite this article: MIN QIAN and FUXI ZHANG (2005). Non-equilibrium of a general stochastic system of coupled oscillators: entropy production rate and rotation numbers.Abstract. In this paper, we address the positive recurrent diffusion process obtained by winding the solutions of a general stochastic system of coupled oscillators along several directions. Two kinds of quantities-the entropy production rate and the rotation numbers, which describe the non-equilibrium of the system from totally different points of vieware calculated and related through an explicit formula.

Some theoretical results of synchronization of a linearly coupled dynamical system with random perturbation on a network

“…Recently, there are some works studying the synchronization on the coupled network with random factors by the approach of stochastic analysis, see [4,5,15,16]. For example, in [4], Berglund, Fernandez and Gentz consider SDE (1.8) of a one-dimension N periodic chain coupled with its nearest neighbors, of which 1 = 0 and f (x) is the negative gradient of a bistable potential 1 4 x 4 − 1 2 x 2 .…”

“…They obtain the precise (asymptotic) synchronizationdesynchronization threshold estimates by some sophisticated mathematical theories, such as metastability and twist map of the integrable system. In [15,16], Qian and Wang, Qian and Zhang study the frequency locking (frequency synchronization) of coupled oscillators under white noises in the view of non-equilibrium physics, such as entropy production. Deng, Ding and Feng consider the case of the stochastic coupled matrix, and some general approach is presented in [5].…”