Abstract
The effects of white noise and global coupling strength on the maximum degree of synchronization in complex networks are explored. We perform numerical simulations of generic oscillator models with both linear and non-linear coupling functions on a broad spectrum of network topologies. The oscillator models include the Fitzhugh–Nagumo model, the Izhikevich model and the Kuramoto phase oscillator model. The network topologies range from regular, random and highly modular networks to scale-free and small-world networks, with both directed and undirected edges. We then study the dependency of the maximum degree of synchronization on the global coupling strength and the noise intensity. We find a general scaling of the synchronizability, and quantify its validity by fitting a regression model to the numerical data.
Highlights
The emergence of collective and synchronous dynamics in large ensembles of coupled units is a ubiquitous phenomenon in nature and engineering
The parameters of the Izhikevich model were chosen such that the model would reproduce a bursting behaviour, in order to further distinguish itself from the Fitzhugh–Nagumo model, expanding the diversity of the oscillator models included in this study
In order to quantify the deviation of the numerical data from the observed functional dependency, we introduce two regression models, which will be fit to the numerical data by a least squares method, and the normalized root-mean-square deviation (NRMSD) will serve as a measure for the difference between the observed values of 〈R〉 and the values implied by the regression models
Summary
The emergence of collective and synchronous dynamics in large ensembles of coupled units is a ubiquitous phenomenon in nature and engineering. The effect of noise on the phasesynchronization of non-linear oscillators has for example been studied in [26], and it is known that white noise prohibits the capability of a system to achieve full synchronization by decreasing the maximum degree of synchronization [3]. It is not clear, how this decrease of synchronizability relates to noise intensity. In order to answer these questions, we develop a numerical simulation framework and study the dependency of the maximum degree of synchronization on the global coupling strength and the noise intensity.
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