We present an analysis of conditions under which the dynamics of a frustrated Kuramoto-or Kuramoto-Sakaguchi-model on sparse networks can be tuned to enhance synchronization. Using numerical optimization techniques, linear stability, and dimensional reduction analysis, a simple tuning scheme for setting node-specific frustration parameters as functions of native frequencies and degrees is devel...

The nonlocal Kuramoto-Sivashinsky equation arises in the modeling of the flow of a thin film of viscous liquid falling down an inclined plane, subject to an applied electric field. In this paper, the authors show that, as the coefficient of the nonlocal integral term goes to zero, the solution trajectories and the maximal attractor of the nonlocal Kuramoto-Sivashinsky equation converge to those...

We begin with formulating the stationary equations of the Kuramoto model as a system of polynomial equations in a novel way. Then, based on an algebraic geometric root count, we give a prescription of computing an upper bound on the number of equilibria of the Kuramoto model for the most general case, i.e., defined on an arbitrary graph and having generic values of natural frequencies and inhom...

The nonlinear Kuramoto equations for n coupled oscillators are derived and studied. The oscillators are defined to be synchronized when they oscillate at the same frequency and their phases are all equal. A control-theoretic viewpoint reveals that synchronized states of Kuramoto oscillators are locally asymptotically stable if every oscillator is coupled to all others. The problem of synchroniz...

We present a class of extended Kuramoto models describing a flocking motion of particles on the infinite cylinder and provide sufficient conditions for the asymptotic formation of locked solutions where the distance between particles remains constant. Our proposed model includes the complex Kuramoto model for synchronization. We also provide several numerical simulation results and compare them...

Considerable attention has been devoted to the different synchronization phenomena [1] in biology. Such as complete synchronization, cluster synchronization, anti-synchronization, and so on[2, 3, 4, 5, 6]. During recent twenty years, phase synchronization has attracted much interest. Many dynamical behaviors in biological systems can be explained by phase synchronization finally[8]. This synchr...

We define a subclass of timed automata, called oscillator timed automata, suitable to model biological oscillators. The semantics of their interactions, parametric w.r.t. a model of synchronization, is introduced. We apply it to the Kuramoto model. Then, we introduce a logic, Kuramoto Synchronization Logic (KSL), and a model checking algorithm in order to verify collective synchronization prope...

In this paper we present a novel approach to model perceptual grouping based on phase and frequency synchronization in a network of coupled Kuramoto oscillators. Transferring the grouping concept from the Competitive Layer Model (CLM) to a network of Kuramoto oscillators, we preserve the excellent grouping capabilities of the CLM, while dramatically improving the convergence rate, robustness to...