Open AccessRobustness in the instability of the incoherent state for the Kuramoto-Sakaguchi-Fokker-Planck equation with frustration
Author(s) -
SeungYeal Ha,
Jaeseung Lee,
Yinglong Zhang
Publication year - 2019
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1533
Subject(s) - instability , frustration , perturbation (astronomy) , nonlinear system , physics , statistical physics , robustness (evolution) , fokker–planck equation , classical mechanics , mathematics , quantum mechanics , differential equation , condensed matter physics , biochemistry , chemistry , gene
We study the robustness in the nonlinear instability of the incoherent state for the Kuramoto-Sakaguchi-Fokker-Planck (KS-FP for short) equation in the presence of frustrations. For this, we construct a new unstable mode for the corresponding linear part of the perturbation around the incoherent state, and we show that the nonlinear perturbation stays close to the unstable mode in some small time interval which depends on the initial size of the perturbations. Our instability results improve the previous results on the KS-FP with zero frustration [J. Stat. Phys. 160 (2015), pp. 477–496] by providing a new linear unstable mode and detailed energy estimates.