An analytical proof for synchronization of stochastic phase oscillator
Y. Sato, T.S. Doan, N.T. The, H.T. Tuan
TL;DR
This paper proves that under certain conditions, stochastic phase oscillators always synchronize due to negative Lyapunov exponents, providing a rigorous analytical foundation for understanding their behavior.
Contribution
It offers an analytical proof that stochastic phase oscillators synchronize under generic conditions, advancing theoretical understanding of stochastic dynamical systems.
Findings
Lyapunov exponent is always negative under generic conditions
Stochastic phase oscillators exhibit synchronization
Provides a rigorous analytical proof of synchronization
Abstract
In this paper, we show that under a generic condition of the coefficient of a stochastic phase oscillator the Lyapunov exponent of the linearization along an arbitrary solution is always negative. Consequently, the generated random dynamical system exhibits a synchronization.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Neural Networks Stability and Synchronization · Stability and Controllability of Differential Equations