Related papers: Dynamical Phase transitions in Kuramoto model with…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
We study a variant of Kuramoto-Sakaguchi model in which oscillators are divided into two groups, each characterized by its coupling constant and phase lag. Specifically, we consider the case that one coupling constant is positive and the…
We study the relaxation dynamics of the inertial Kuramoto model toward a phase-locked state from a generic initial phase configuration. For this, we propose a sufficient framework in terms of initial data and system parameters for…
We consider chimera states of coupled identical phase oscillators where some oscillators are phase synchronized while others are desynchronized. It is known that chimera states of non-locally coupled Kuramoto--Sakaguchi oscillators in…
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…
The emergence of synchrony essentially underlies the functionality of many systems across physics, biology and engineering. In all established synchronization phase transitions so far, a stable synchronous state is connected to a stable…
The Kuramoto model has been introduced to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. The model consists of $N$ interacting oscillators on the one dimensional sphere $\mathbf{S}^{1}$, driven…
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble…
We investigate the continuum q-Potts model at its transition point from the disordered to the ordered regime, with particular emphasis on the coexistence of disordered and ordered phases in the high-q case. We argue that occurrence of phase…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
We study the asymptotic clustering (phase-locking) dynamics for the Kuramoto model. For the analysis of emergent asymptotic patterns in the Kuramoto flow, we introduce the pathwise critical coupling strength which yields a sharp transition…
We have examined the synchronization and de-synchronization transitions observable in the Kuramoto model with a standard pair-wise first harmonic interaction plus a higher order (triadic) symmetric interaction for unimodal and bimodal…
Using two models of opinion dynamics, the $q$-voter model with independence and the $q$-voter model with anticonformity, we discuss how the change of disorder from annealed to quenched affects phase transitions on networks. To derive phase…
We present a detailed analysis of the stability of synchronized solutions to the Kuramoto system of oscillators. We derive an analytical expression counting the dimension of the unstable manifold associated to a given stationary solution.…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically…
We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the…
We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical…
A class of adaptation functions is found for which a synchronous oscillation mode exists in the network of phase oscillators with triadic couplings. It is shown that the destruction of the synchronous mode occurs differently for networks…