Fokker-Planck dynamics of two coupled van der Pol oscillators subjected to stochastic forcing

被引:0
作者
Lee, Minwoo [1 ,2 ]
Gupta, Vikrant [3 ,4 ]
Li, Larry K. B. [2 ,5 ]
机构
[1] Hanbat Natl Univ, Dept Mech Engn, Daejeon 34158, South Korea
[2] Hong Kong Univ Sci & Technol, Dept Mech & Aerosp Engn, Clear Water Bay, Hong Kong, Peoples R China
[3] Southern Univ Sci & Technol, Guangdong Hong Kong Macao Joint Lab Data Driven Fl, Hong Kong 518055, Guangdong, Peoples R China
[4] Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen, Peoples R China
[5] Hong Kong Univ Sci & Technol, Guangdong Hong Kong Macao Joint Lab Data Driven Fl, Clear Water Bay, Hong Kong, Guangdong, Peoples R China
关键词
NOISE-INDUCED DYNAMICS; SYSTEM-IDENTIFICATION; COHERENCE RESONANCE; AMPLITUDE DEATH; SYNCHRONIZATION; BIFURCATIONS;
D O I
10.1103/PhysRevE.110.044202
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We present probabilistic solutions to a pair of mutually coupled Van der Pol oscillators subjected to stochastic forcing. We consider three different types of coupling: reactive, dissipative, and nonlinear coupling. Using stochastic averaging, we derive the stationary Fokker-Planck equation for each oscillator, yielding a probability density function for the fluctuation amplitude. For each coupling type, we numerically validate the Fokker-Planck solutions for different noise levels and coupling strengths, with a focus on the stochastic and bifurcation characteristics. The validated analytical expressions derived in this study could serve to improve the prediction and control of a generic class of coupled oscillator systems operating near the Hopf point in the presence of noise.
引用
收藏
页数:12
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