2018/05/09 by Hui Wu, Wu, Hui, Mukesh Dhamala +1 · 2 citations
Computer Science · Neuroscience · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #nlin.AO #nlin.CD
paper · pdf · doi:10.48550/arxiv.1805.03510
arxiv created 2018/05/09 · openalex publication_date 2018/05/09 · arxiv updated 2018/05/10 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28
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 individual frequencies, coupling, interaction time delays and network structure-function relation. Here, using a generalized Kuramoto model of time-delay coupled phase oscillators with frequency-weighted coupling, we study the stability of incoherent and coherent states and the transitions to or out of explosive (abrupt, first-order like) phase synchronization. We analytically derive the exact formulas for the critical coupling strengths at different time delays in both directions of increasing (forward) and decreasing (backward) coupling strengths. We find that time-delay does not affect the transition for the backward direction but shifts the transition for the forward direction of increasing coupling strength. These results provide valuable insights into our understanding of dynamical mechanisms for explosive synchronization in presence of often unavoidable time delays present in many physical and biological systems.