Related papers: Stochastic Kuramoto oscillators with inertia and h…
We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
We study Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies with nearest neighbor interactions. We derive the analytical expressions for the common frequency in the case of phase-locked motion and for the…
We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous…
Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. We derive conditions…
We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with…
We investigate group-level synchronization between oscillator groups induced by common noise in the absence of inter-group coupling. Each group receives a common noise shared by all its oscillators and independent local noise inputs to…
The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis…
In this article, we study the scrambling dynamics in supersymmetric quantum mechanical systems. The eigenstate representation of such supersymmetric systems allows us to present an explicit form of the $2N$-point out-of-time-order…
The high-dimensional generalization of the one-dimensional Kuramoto paradigm has been an essential step in bringing about a more faithful depiction of the dynamics of real-world systems. Despite the multi-dimensional nature of the…
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses…
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…
Recently, the explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works investigate Kuramoto-type models, where only phase variables are…
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative noise arising from a control parameter of the system. Contrary to the…
We study the noisy Kuramoto model for two interacting communities of oscillators, where we allow the interaction in and between communities to be positive or negative (but not zero). We find that, in the thermodynamic limit where the size…
We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between…
The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response…
Most studies of collective phenomena in oscillator networks focus on directly coupled systems as exemplified by the classical Kuramoto model. However, there are growing number of examples in which oscillators interact indirectly via a…
We study the overdamped version of two coupled anharmonic oscillators under the influence of both low- and high-frequency forces respectively and a Gaussian noise term added to one of the two state variables of the system. The dynamics of…
Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with…