Lee Minwoo, Gupta Vikrant, Li Larry K B
Department of Mechanical Engineering, <a href="https://ror.org/00x514t95">Hanbat National University</a>, Daejeon 34158, South Korea.
Department of Mechanical and Aerospace Engineering, <a href="https://ror.org/00q4vv597">Hong Kong University of Science and Technology</a>, Clear Water Bay, Hong Kong.
Phys Rev E. 2024 Oct;110(4-1):044202. doi: 10.1103/PhysRevE.110.044202.
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.
我们给出了一对受随机激励的相互耦合的范德波尔振子的概率解。我们考虑三种不同类型的耦合：反应性耦合、耗散性耦合和非线性耦合。利用随机平均法，我们推导出了每个振子的稳态福克-普朗克方程，得到了波动幅度的概率密度函数。对于每种耦合类型，我们针对不同的噪声水平和耦合强度对福克-普朗克解进行了数值验证，重点关注随机和分岔特性。本研究中得到的经过验证的解析表达式可用于改进对一类在存在噪声情况下接近霍普夫点运行的耦合振子系统的预测和控制。
