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Open AccessArticle

Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations

by 1, 2,* and 1
1
Research Center of Applied Mechanics, School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, China
2
State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, China
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(6), 280; https://doi.org/10.3390/e19060280
Received: 17 May 2017 / Revised: 14 June 2017 / Accepted: 14 June 2017 / Published: 15 June 2017
(This article belongs to the Special Issue Complex Systems, Non-Equilibrium Dynamics and Self-Organisation)
A semi-analytical method is proposed to calculate stochastic quasi-periodic responses of limit cycles in non-equilibrium dynamical systems excited by periodic forces and weak random fluctuations, approximately. First, a kind of 1/N-stroboscopic map is introduced to discretize the quasi-periodic torus into closed curves, which are then approximated by periodic points. Using a stochastic sensitivity function of discrete time systems, the transverse dispersion of these circles can be quantified. Furthermore, combined with the longitudinal distribution of the circles, the probability density function of these closed curves in stroboscopic sections can be determined. The validity of this approach is shown through a van der Pol oscillator and Brusselator. View Full-Text
Keywords: weak fluctuation; non-equilibrium system; quasi-periodic; stochastic sensitivity function; probability density function weak fluctuation; non-equilibrium system; quasi-periodic; stochastic sensitivity function; probability density function
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Guo, K.; Jiang, J.; Xu, Y. Approximation of Stochastic Quasi-Periodic Responses of Limit Cycles in Non-Equilibrium Systems under Periodic Excitations and Weak Fluctuations. Entropy 2017, 19, 280.

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