Nonlinear Instability of the Incoherent State for the Kuramoto-Sakaguchi-Fokker-Plank Equation

作者：Ha Seung Yeal; Xiao Qinghua^*

来源：Journal of Statistical Physics, 2015, 160(2): 477-496.

DOI：10.1007/s10955-015-1270-5

• Kinetic Kuramoto model
• Kuramoto-Sakaguchi-Fokker-Plank model
• Nonlinear instability
• Incoherent solution
• Synchronization

We study the nonlinear instability of the incoherent solution to the Kuramoto-Sakaguchi-Fokker-Plank (KSFP) equation in a large coupling strength regime. For our instability analysis, we construct an approximate, exponentially growing perturbation mode using an elementary energy method. This method does not require spectral information from the linearized KSFP equation or an explicit growing solution for the corresponding linear equation. When the distribution function of oscillator's natural frequencies is either a Dirac measure or a bounded function with a compact support (in a small interval around the origin), the incoherent solution is nonlinearly unstable depending on the relative sizes of the coupling strength and diffusion coefficient.

• 出版日期2015-7
• 单位中国科学院武汉物理与数学研究所