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

作者：Guo, Kongming; Jiang, Jun^*; Xu, Yalan

来源：Entropy, 2017, 19(6): 280.

DOI：10.3390/e19060280

• weak fluctuation
• non-equilibrium system
• quasi-periodic
• stochastic sensitivity function
• probability density function

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.

• 出版日期2017-6
• 单位西安电子科技大学; 西安交通大学