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The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually…
Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…
We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We…
While considerable progress has been made in the analysis of large systems containing a single type of coupled dynamical component (e.g., coupled oscillators or coupled switches), systems containing diverse components (e.g., both…
The interdependence between an individual strategy decision and the resulting change of environmental state is often a subtle process. Feedback-evolving games have been a prevalent framework for studying such feedback in well-mixed…
When modeling the classical Kuramoto model, one of the key features is the tendency to synchronize. Accordingly, the most well-adopted choice of the coupling function is the sine function. Due to the oddness of the sine function, the…
The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a…
The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…
The synchronization of human networks is essential for our civilization, and understanding the motivations, behavior, and basic parameters that govern the dynamics of human networks is important in many aspects of our lives. Human ensembles…
The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of…
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…
The sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand,…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple…
Synchronization, cooperation, and chaos are ubiquitous phenomena in nature. In a population composed of many distinct groups of individuals playing the prisoner's dilemma game, there exists a migration dilemma: No cooperator would migrate…
Situations of conflict giving rise to social dilemmas are widespread in society and game theory is one major way in which they can be investigated. Starting from the observation that individuals in society interact through networks of…
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…