Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

Abstract

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdős-Rényi (ER) networks in detail. Depending on the degree distribution exponent (γ) of SF networks and phase-frustration parameter, the population undergoes from first order transition (explosive synchronization (ES)) to second order transition and vice versa. In ER networks transition is always second order irrespective of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self consistent equations considering the vanishing order parameter limit.

Repulsive synchronization in complex networks

“…Because this repulsive synchronization, therefore, cannot be characterized by the order parameter r, we introduce the dispersion of effective frequencies σ to describe it. However, since σ is defined statistically, the Chaos ARTICLE scitation.org/journal/cha classical analysis 25 cannot be used, hence a new approach is expected in the future. The repulsive synchronization is found to exist in complex networks with different structures, such as BA, ER, scale-free networks, and small-world networks, so may be prevalent in complex networks.…”

“…Futhermore, it has shown that with the repulsive interactions, the system will turn to partial synchronization from fully synchronized state, and also traveling wave is observed. 23 Recently, some works have investigated about synchronizing phase frustrated Kuramoto oscillators [24][25][26] and found a complex relationship between the phase shifts and the synchronization phase transition. In these works, the phase shift is focused on the range of [0, π/2].…”

Predicting bursting in a complete graph of mixed population through reservoir computing

“…is the DC bias current. It is to be mentioned that the isolated RSCJ model has similarities with the Sakaguchi-Kuramoto phase model with inertia [43][44][45] and also with the working model of a power grid [46]. In the absence of coupling ( = 0) and a = 1.5, each node can reveal two types of dynamics: oscillatory spiking behavior (I i > 1.0) and a quiescent state (I i < 1.0).…”

Synchronization in starlike networks of phase oscillators

“…Equation ( 2) describes a set of Kuramoto-Sakaguchi oscillators in a star network with the assumption of frequencyweighted correlations [24][25][26][27][28]. Since the Kuramoto-like model in the star network with frequency-degree correlation is given byφ…”