A Convergence Result for the Kuramoto Model with All-to-All Coupling

نویسندگان

  • Mark Verwoerd
  • Oliver Mason
چکیده

We prove a convergence result for the standard Kuramoto model with all-to-all coupling. Specifically, we show that the critical coupling strength associated with the onset of completely phase-locked behaviour converges in probability as the number of oscillators tends to infinity.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

همگام‌سازی 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 کامل

Synchronization and semistability analysis of the Kuramoto model of coupled nonlinear oscillators

An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the stability and convergence in a network of coupled oscillators described by the Kuramoto model. We consider networks with finite number of oscillators, arbitrary ...

متن کامل

همگام‌سازی در مدل کوراموتو روی شبکه‌های پیچیده با توزیع فرکانس ذاتی دوقله‌ای

In this work, we study the Kuramoto model on scale-free, random and small-world networks with bimodal intrinsic frequency distributions. We consider two models: in one of them, the coupling constant of the ith oscillator is independent of the number of oscillators with which the oscillator interacts, and in the other one the coupling constant is renormalized with the number of oscillators with ...

متن کامل

Fast and Slow Relaxations to Bi-cluster Configurations for the Ensemble of Kuramoto Oscillators

We present asymptotic relaxation estimates to bi-cluster configurations for the ensemble of Kuramoto oscillators with two different natural frequencies which have been observed in numerical simulations. We provide a set of initial configurations with a positive Lebesgue measure in T leading to bi-(point) cluster configurations consisting of linear combinations of two Dirac measures in super-thr...

متن کامل

The Spectrum of the Partially Locked State for the Kuramoto Model

We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics, and also because it provides a beautiful connection between nonlinear dynamics and statistical mechanics. The model consists of a large population of phase o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • SIAM J. Applied Dynamical Systems

دوره 10  شماره 

صفحات  -

تاریخ انتشار 2011