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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 investigate the role of frequency-weighted interactions in a solvable model of one-dimensional (1D) swarmalators confined to a ring, where both spatial and phase couplings are scaled by the heterogeneous natural frequencies of individual…
The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators…
The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an…
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…
Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…
We consider the effect of an external periodic force on chimera state in the phase oscillator model proposed by Abrams et al. [Phys. Rev. Lett, v. 101, 00319007 (2008)]. Using the Ott--Antonsen reduction the dynamical equations for the…
We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially-periodic force field can…
We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and…
We introduce a system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal phase $\phi_i$. The disks experience an additional attractive or repulsive force with neighboring disks…
We study a system of interacting self-propelled particles whose walking velocity depends on the stage of the locomotion cycle. The model introduces a phase equation in the optimal velocity model for vehicular traffic. We find that the…
We study the 1d swarmalator model in the continuum limit. We examine the stability of its collective states which have compact support: synchrony, where the swarmalators lie in two sync dots (zero dimensional support), and the phase wave,…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
Recent studies of dynamic properties in complex systems point out the profound impact of hidden geometry features known as simplicial complexes, which enable geometrically conditioned many-body interactions. Studies of collective behaviours…
Systems of self-propelled particles are known for their tendency to aggregate and to display swarm behavior. We investigate two model systems, self-propelled rods interacting via volume exclusion, and sinusoidally-beating flagella embedded…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
A system's response to external periodic changes can provide crucial information about its dynamical properties. We investigate the synchronization transition, an archetypical example of a dynamic phase transition, in the framework of such…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…