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We study the global bifurcations of frequency weighted Kuramoto model in low-dimension for network of fully connected oscillators. To study the effect of non-zero-centered frequency distribution, we consider two symmetric Lorentzians as an example. We derive the stability diagram of the system and show that the infinite-dimensional problem reduces to a flow in four dimensions. Using the system symmetries, it can be further reduced to two dimensions. Using this analytic framework, we obtain bifurcation boundaries of the system, which is compatible with our numeric simulations. We show that the system has three types of transitions to synchronized state for different parameters of the frequency distribution: (1) a two-step transition, representative of standing waves, (2) a continuous transition, as in the classical Kuramoto model, and (3) a first-order transition with hysteresis. Numerical simulations are also conducted to confirm analytic results.
We study a variant of Kuramoto-Sakaguchi model in which oscillators are divided into two groups, each characterized by its coupling constant and phase lag. Specifically, we consider the case that one coupling constant is positive and the other negati
The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important in applica
We examine analytically and numerically a variant of the stochastic Kuramoto model for phase oscillators coupled on a general network. Two populations of phased oscillators are considered, labelled `Blue and `Red, each with their respective networks,
The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture the colle
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order interacti