Abstract Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based a recent formulation weighted simplicial complexes phases supported simplices any order k , we introduce linear and non-linear frustration terms independent orientation + 1 s...

In this short note, we discuss the basin of attractions for many Kuramoto oscillators with unidirectional couplings. For attractive and repulsive couplings, we present proper subsets for the basin of attractions, which are independent of the number of oscillators.

We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing insulat...

We consider the Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and...

We present a computational study of a simple finite-dimensional feedback control algorithm for stabilizing solutions of infinite-dimensional dissipative evolution equations such as reaction-diffusion systems, the Navier-Stokes equations and the Kuramoto-Sivashinsky equation. This feedback control scheme takes advantage of the fact that such systems possess finite number of determining parameter...

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillato...