Related papers: Binary system modes of matrix-coupled multidimensi…
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous,…
The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…
We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…
This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective…
Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…
We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the…
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…
Coordination is ubiquitous in living systems. Existing theoretical models of coordination -- from bacteria to brains -- focus on either gross statistics in large-scale systems ($N\rightarrow\infty$) or detailed dynamics in small-scale…
Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…
In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static…
Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move…
Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…
Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity…
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 explore synchronization transitions in even-$D$-dimensional generalized Kuramoto oscillators on both complete graphs and $d$-dimensional lattices. In the globally coupled system, analytical expansions of the self-consistency equations,…