2015/07/22 by Walid OUKIL, Oukil, W, Kessi, A +1
Computer Science · Neuroscience · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation
paper · doi:10.48550/arxiv.1507.06061
openalex publication_date 2015/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider N oscillators coupled by a mean field as in the Winfree model. The model is governed by two parameters: the coupling strength κ and the spectrum width γ of the frequencies of each oscillator. In the uncoupled regime, κ=0, each oscillator possesses its own natural frequency, and the difference between the phases of any two oscillators grows linearly in time. We say that N oscillators are synchronized if the difference between any two phases is uniformly bounded in time. We identify a new hypothesis for the existence of synchronization. The domain in (γ,κ) of synchronization contains coupling values that are both weak and strong. Moreover the domain is independent of the number of oscillators and the distribution of the frequencies. We give a numerical counter-example which shows that this hypothesis is necessary for the existence of synchronization.