Effects of frustration on explosive synchronization

Abstract

In this study, we consider the emergence of explosive synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and frustration is included in the system. This assumption can enhance or delay the explosive transition to synchronization. Interestingly, a de-synchronization phenomenon occurs and the type of phase transition is also changed. Furthermore, we provide an analytical treatment based on a star graph, which resembles that obtained in scale-free networks. Finally, a self-consistent approach is implemented to study the de-synchronization regime. Our findings have important implications for controlling synchronization in complex networks because frustration is a controllable parameter in experiments and a discontinuous abrupt phase transition is always dangerous in engineering in the real world.

Order parameter analysis of synchronization transitions on star networks

“…The star topology is the simplest while the key topology in describing the heterogeneity property of complex networks such as the scale-free networks [33][34][35][36]. In this paper, we study the collective states and the abundant transitions among these states on a star network by considering the effect of the phase shift among coupled oscillators [23,26,[37][38][39]. The dynamics of star networks of oscillators is analytically studied by building the equations of motion of the order parameter for networks with a finite size, which accomplishes a great reduction from microscopic high-dimensional phase dynamics of coupled oscillators to a macroscopic low-dimensional dynamics.…”

A Nanotechnology-Ready Computing Scheme based on a Weakly Coupled Oscillator Network

“…1(b), especially when several pairs of core oscillators are involved. Indeed, while interaction phase-shifts do not prevent synchronization between two oscillators, frustrations a rise when several oscillators are involved in the synchronization process as seen in other contexts in refs 53 and 54. This phenomenon is critical in the context of the stimuli-induced core oscillator synchronizations, as at least three oscillators (2 core and 1 input) are involved.…”

Explosive synchronization of multi-layer frequency-weighted coupled complex systems*

“…With the intensive investigation of ES and improvements of the Kuramoto model, many factors affecting ES have been considered, such as frustration, external force, pacemaker, and frequency distribution. [24][25][26][27][28] Although many related works on ES have been published, these works are all based on single-layer networks. In recent years, the research of synchronization on complex network has gradually shifted from the single-layer network to the multilayer network.…”