Journal ArticleDOI
Influence of noise on the synchronization of the stochastic Kuramoto model.
TLDR
The Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise is considered and the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise is studied.Abstract:
We consider the Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and find that the threshold of synchronization strongly depends on the nature of the noise. It is found to be lower for both the Ornstein-Uhlenbeck and non-Gaussian processes compared to the case of white noise. A finite correlation time also favors the achievement of the full synchronization of the system, in contract to the white noise process, which does not allow that. Finally, we discuss possible applications of the stochastic Kuramoto model to oscillations taking place in biochemical systems.read more
Citations
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Journal ArticleDOI
Synchronization in complex networks of phase oscillators: A survey
Florian Dörfler,Francesco Bullo +1 more
TL;DR: This survey reviews the vast literature on the theory and the applications of complex oscillator networks, focusing on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology.
Journal ArticleDOI
Multidimensional stationary probability distribution for interacting active particles.
TL;DR: In this paper, the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential is derived.
Journal ArticleDOI
Multidimensional Stationary Probability Distribution for Interacting Active Particles
TL;DR: The stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential is derived based on a multidimensional version of the Unified Colored Noise Approximation.
Journal ArticleDOI
Stability measures in metastable states with Gaussian colored noise.
TL;DR: Two dynamical regimes characterized by weak and strong correlated noises, depending on the value of tau(c) with respect to the relaxation time of the system, are distinguished.
Journal ArticleDOI
Paths to globally generalized synchronization in scale-free networks.
TL;DR: The auxiliary-system approach is applied to study paths to globally generalized synchronization in scale-free networks of identical chaotic oscillators, including Hénon maps, logistic maps, and Lorentz oscillators to understand the synchronization process in complex networks.
References
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Reaction-rate theory: fifty years after Kramers
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On the Theory of the Brownian Motion
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The Kuramoto model: A simple paradigm for synchronization phenomena
TL;DR: In this paper, a review of the Kuramoto model of coupled phase oscillators is presented, with a rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years.
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From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators
TL;DR: In this article, the authors review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto's work to Crawford's recent contributions.