Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-12-13
Physics
Condensed Matter
Statistical Mechanics
15 pages, 6 figures (10 eps files), 2 tables; submitted to JSP
Scientific paper
We discuss the {\it nonlinear stability} of phase-locked states for globally coupled nonlinear oscillators with finite inertia, namely the modified Kuramoto model, in the context of the robust $\ell^{\infty}$-norm. We show that some classes of phase-locked states are orbitally $\ell{\infty}$-stable in the sense that its small perturbation asymptotically leads to only the phase shift of the phase-locked state from the original one without changing its fine structures as keeping the same suitable coupling strength among oscillators and the same natural frequencies. The phase shift is uniquely determined by the average of initial phases, the average of initial frequencies, and the strength of inertia. We numerically confirm the stability of the phase-locked state as well as its uniqueness and the phase shift, where various initial conditions are considered. Finally, we argue that some restricted conditions employed in the mathematical proof are not necessary, based on numerical simulation results.
Choi Chulho
Choi Young-Pil
Ha Meesoon
Ha Seung-Yeal
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