Related papers: Synchronization in a Kuramoto Mean Field Game
In this paper, we investigate how the self-synchronization property of a swarm of Kuramoto oscillators can be controlled and exploited to achieve target densities and target phase coherence. In the limit of an infinite number of…
We analyse the collective behavior of a mean-field model of phase-oscillators of Kuramoto-Daido type coupled through pairwise interactions which depend on phase differences: the coupling function is composed of three harmonics. We provide…
The Kuramoto model is a canonical framework for analyzing phase synchronization, yet its utility is restricted to the vicinity of the oscillator's unperturbed limit cycle. Here, we present a method to construct coupled-oscillator models…
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…
Despite being under intense scrutiny for 50 years, the Kuramoto oscillator model has remained a quintessential representative of non-equilibrium phase transitions. One of the reasons for its enduring relevance is the apparent lack of an…
We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into…
We study the homogeneous Kuramoto model on a graph and the geometry of its underlying optimization landscape $\min_{\boldsymbol \theta \in \mathbb R^n}-\sum_{1\leq i,j\leq n} A_{ij}\cos(\theta_i-\theta_j).$ This problem admits a dual…
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics, and biology. The Kuramoto model has emerged as a…
We consider a class of $N$-player games and mean-field games of singular controls with ergodic performance criterion, providing a benchmark case for irreversible investment games featuring mean-field interaction and strategic…
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter…
We present a novel method to compute the phase space distribution in the nonequilibrium stationary state of a wide class of mean-field systems involving rotators subject to quenched disordered external drive and dissipation. The method…
The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…
The hypothesis, that cortical dynamics operates near criticality also suggests, that it exhibits universal critical exponents which marks the Kuramoto equation, a fundamental model for synchronization, as a prime candidate for an underlying…
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…
What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated…
We consider a recently introduced $D$-dimensional generalized Kuramoto model for many $(N\gg 1)$ interacting agents in which the agent states are $D$-dimensional unit vectors. It was previously shown that, for even $D$, similar to the…
In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…
The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…