In this paper, we intend to investigate the effects of both heterogeneity and asymmetric coupling on the collective behaviors of Kuramoto oscillators, and reveal the processes how the synchronization transits to
In this paper, we consider Kuramoto-type networks with coupling weights governed by a phase-difference-dependent plasticity (PDDP) rule, first introduced in Ref.10. The PDDP rule is built similarly to the STDP rule, but instead of the time difference, the phase difference of the oscillators is...
Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several factors, such as in
It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from incoherency to synchronization occurs. This paper features four contributions. First, we characterize and distinguish the different notions of synchronization used throughout the ...
oscillatorssynchronisation/ critical coupling strengthKuramoto oscillatorsone-dimensional chainperiodic boundary conditionsfrequency synchronizationmathematical constraint conditionsSynchronization in a one-dimensional chain of Kuramoto oscillators with periodic boundary conditions is studied. An algorithm to rapidly ...
The Kuramoto model of coupled oscillators with a bi-harmonic coupling function. Physica D 289, 18-31, doi:10.1016/j.physd.2014.09.002 (2014).Komarov M, Pikovsky A. The Kuramoto model of coupled oscillators with a bi-harmonic coupling function. Physica D: Nonlinear Phenomena. 2014;289:18-...
We study the generalized Kuramoto model of coupled phase oscillators with a finite size, and discuss the asymptotic complete phase鈥揻requency synchronization. The generalized Kuramoto model has inherent difficulties in mathematical approaches that this model is governed by nonlinear equations and the ...
The Kuramoto model of coupled oscillators with a bi-harmonic coupling function. Physica D 289, 18-31, doi:10.1016/j.physd.2014.09.002 (2014).Komarov M, Pikovsky A. The Kuramoto model of coupled oscillators with a bi-harmonic coupling function. Physica D: Nonlinear Phenomena. 2014;289:18-...
While this approach can also be applied to systems with a finite number of oscillators, discussion here will focus on the reformulated model in the continuum limit, the regime of validity of the original Kuramoto solution. This new approach allows one to solve explicitly for the sy...
Protopopescu, Controlling synchrony in a network of Kuramoto oscillators with time-varying coupling. Physica D, 301-302, pp. 36-47, 2015.R. Leander, S. Lenhart, and V. Protopopescu. Controlling synchrony in a network of Kuramoto oscillators. Physica D: Nonlinear Phenomena, 301-302:36-47,...