Abstract
In this work, we study the Sakaguchi-Kuramoto model with natural frequency following a bimodal distribution. By using Ott-Antonsen ansatz, we reduce the globally coupled phase oscillators to low dimensional coupled ordinary differential equations. For symmetrical bimodal frequency distribution, we analyze the stabilities of the incoherent state and different partial synchronous states. Different types of bifurcations are identified and the effect of the phase lag on the dynamics is investigated. For asymmetrical bimodal frequency distribution, we observe the revival of the incoherent state, and then the conditions for the revival are specified.
Highlights
Collective behaviors emerged out of a large number of interacting units are common in nature
Each unit is treated as a phase oscillator, which is valid for the weak coupling situation where the amplitude information of each unit is inessential to the collective behaviors
The dynamics of each phase oscillator is solely determined by its natural frequency and in turn the frequencies of all oscillators are drawn from a prescribed frequency distribution function g(ω)
Summary
Collective behaviors emerged out of a large number of interacting units are common in nature. As one type of collective behavior characterizing the phase coherence in nonidentical units, synchronization is well recognized in various systems such as fireflies flashing in unision [1, 2], applauding persons in a large audience [3], pedestrians [4, 5], and others [6]. The dynamics of each phase oscillator is solely determined by its natural frequency and in turn the frequencies of all oscillators are drawn from a prescribed frequency distribution function g(ω). The coupling between units is assumed to be a global one and takes the form of a sinusoidal function with the same strength K. The coupling strength together with the frequency distribution determine the dynamics of KM
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