The study of synchronization in generalized Kuramoto models has witnessed an intense boost in the last decade. Several collective states were discovered, such as partially synchronized, chimera, π or traveling wave states. We here consider two populations of globally coupled conformist and contrarian oscillators (with different, randomly distributed frequencies), and explore the effects of a fr...

The Kuramoto-Sivashinsky equation arises in a variety of applications, among which are modeling reaction-diffusion systems, flame-propagation and viscous flow problems. It is considered here, as a prototype to the larger class of generalized Burgers equations: those consist of quadratic nonlinearity and arbitrary linear parabolic part. We show that such equations are well-posed, thus admitting ...

A generalized Kuramoto model of coupled phase oscillators with a slow varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling strengthens for synchronized oscillators and weakens for nonsynchronized pairs. The system possesses a family of stable solutions corresponding to synchronized...

Networks of coupled phase oscillators play an important role in the analysis emergent collective phenomena. In this article, we introduce generalized m-splay states constituting a special subclass phase-locked with vanishing mth order parameter. Such typically manifest incoherent dynamics, and they often create high-dimensional families solutions (splay manifolds). For general class oscillator ...

We modify the Kuramoto model for synchronization on complex networks by introducing a gauge term that depends on the edge betweenness centrality (BC). The gauge term introduces additional phase difference between two vertices from 0 to π as the BC on the edge between them increases from the minimum to the maximum in the network. When the network has a modular structure, the model generates the ...

The Kuramoto model, first proposed in 1975, consists of a population of sinusoidally coupled oscillators with random natural frequencies. It has served as an idealized model for coupled oscillator systems in physics, chemistry, and biology. This paper addresses a long-standing problem about the infinite-N Kuramoto model, which is to describe the asymptotic behavior of the order parameter for th...

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretical extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally reduced description for such systems. The neglected degrees of freedom by this reduction are replaced by a systematically defined stochastic process under a co...

The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. system approached in the weakly coupled approximation as units. Instead global couplings, nearest-neighbor interaction assumed. Units pairwise by Kuramoto term driven their differences. exhibits rich set behaviors depending on balance be...

In this article we study the solution of the Kuramoto–Sivashinsky equation on a bounded interval subject to a random forcing term. We show that a unique solution to the equation exists for all time and depends continuously on the initial data.