Abstract
The Sakaguchi-Kuramoto model is a modification of the well-known Kuramoto model, in which a frustration factor is added to the coupling term of each phase oscillator. The added frustration factor destroys the gradient structure, but the modified model is more widely used in practice. In this paper, we study how frustration factors influence the synchronization transition of coupled oscillators in the Sakaguchi-Kuramoto model with frequency mismatch rules. The results show that in the system of coupled oscillators, the frustration factor manifests a disorder field, which restrains the explosive synchronization and weakens the synchronization ability of the whole network. In addition, it is found that the frequency synchronization can not be detected by the common phase order parameter, so a new index is introduced to characterize the degree of frequency synchronization. As an example, at the end of the paper, we theoretically analyze the synchronization dynamics of two-oscillator system, and indirectly verify the correctness of simulations for the multi-body system.
Highlights
Synchronization is a very common phenomenon in different fields, such as physics, chemistry, biology and so on
The Sakaguchi-Kuramoto model is a modification of the well-known Kuramoto model, in which a frustration factor is added to the coupling term of each phase oscillator
We mainly focus on the influence of frustration factors on the synchronization transition of coupled oscillators
Summary
Synchronization is a very common phenomenon in different fields, such as physics, chemistry, biology and so on. It is the basic mechanism to reveal the collective phenomenon in nature and man-made systems. Among these models, Kuramoto model is the simplest in which the dynamics of an oscillator are described by only a phase variable [3] [4] [5]. The Kuramoto model introduces statistical methods, and links the synchronous behavior in the field of dynamics with the non-equilibrium phase transition in statistical physics
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