Related papers: Fixed points and stability in the two-network frus…
We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the…
We present a detailed analysis of the stability of synchronized solutions to the Kuramoto system of oscillators. We derive an analytical expression counting the dimension of the unstable manifold associated to a given stationary solution.…
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…
We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of…
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…
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…
We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady state solutions called twisted states. We prove a sufficient…
We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two…
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 celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
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…
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 study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…
We introduce a generalization of the Kuramoto model by explicit consideration of time-dependent parameters. The oscillators' natural frequencies and/or couplings are supposed to be influenced by external, time-dependant fields, with…
In this note we show that for the Kuramoto model defined in a simple undirected graph it is possible to decide which nodes form the core of the network. The set of core-nodes is defined by its relevance to the phase synchronisation process.
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization…