Related papers: Synchronization in a Kuramoto Mean Field Game
A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…
We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality…
A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
We consider the mean-field noisy Kuramoto-Daido model, which is a McKean-Vlasov equation on the circle with bimodal interaction $W(\theta)=\cos\theta+m\cos2\theta$ for $m\ge 0$ and interaction strength $K$, generalizing the celebrated noisy…
Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and…
In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest neighbor interactions and dichotomous noise. In the nonequilibrium…
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…
The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…
In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled…
In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the…
In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an…
The cluster synchronization (CS) is a very important characteristic for the higher harmonic cou- pling Kuramoto system. A novel method from the symmetry transformation is provided, and it gives CS a profoundly mathematical explanation and…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…