The Kuramoto model with distributed shear
نویسندگان
چکیده
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter synchronization and yield qualitatively different phase diagrams. The Ott-Antonsen ansatz allows us to obtain analytical results for a specific family of joint distributions. We also derive, using linear stability analysis, general formulae for the stability border of incoherence. Copyright c © EPLA, 201
منابع مشابه
Shear diversity prevents collective synchronization.
Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of mutual interactions. If the oscillators have distributed natural frequencies and common shear (or nonisochronicity), the transition from incoherence to collective synchronization is known to occur at large enough values of the coupling strength. However, here we demonstrate that shear diversity ...
متن کاملهمگامسازی در مدل کوراموتو با نیروی وابسته به زمان در شبکه‌های پیچیده
In this paper, a generalization of the Kuramoto model is introduced by explicit consideration of deterministically time-varying periodic external force. In this model, the oscillator's natural frequencies and amplitude of collective oscillations are influenced by external forces with constant or random strengths. Then, the synchronization behavior of forced Kuramoto model is studied in some com...
متن کاملApplication of Daubechies wavelets for solving Kuramoto-Sivashinsky type equations
We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition. Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method. The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method.
متن کاملOscillator Synchronization
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...
متن کاملStability of a Distributed Generation Network Using the Kuramoto Models
We derive a Kuramoto-like equation from the Cardell-Ilic distributed electrical generation network and use the resulting model to simulate the phase stability and the synchronization of a small electrical grid. In our model nodes are arranged in a regular lattice; the strength of their couplings are randomly chosen and allowed to vary as square waves. Although the system undergoes several synch...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011