Explosive behaviour in networks of Winfree oscillators

Abstract

We consider directed networks of Winfree oscillators with power law distributed in- and out-degree distributions. Gaussian and power law distributed intrinsic frequencies are considered, and these frequencies are positively correlated with oscillators' in-degrees. The Ott/Antonsen ansatz is used to derive degree-based mean field equations for the expected dynamics of networks, and these are numerically analysed. In a variety of cases "explosive" transitions between either two different steady states or between a steady state and a periodic solution are found, and these transitions are explained using bifurcation theory.

arXiv commentTo appear in Chaos, Solitons and Fractals

References in corpus (18)

• The structure and function of complex networks
• Explosive Synchronization Transitions in Scale-free Networks
• Long Time Evolution of Phase Oscillator Systems
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Explosive Phenomena in Complex Networks
• Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
• Low-dimensional dynamics of populations of pulse-coupled oscillators
• Explosive transitions to synchronization in networked phase oscillators
• A Universal Route to Explosive Phenomena
• Disorder induces explosive synchronization
• Mean field theory of assortative networks of phase oscillators
• Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses
• The role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue
• Modeling the Network Dynamics of Pulse-Coupled Neurons
• Frequency assortativity can induce chaos in oscillator networks
• The Winfree model with heterogeneous phase-response curves: Analytical results
• The effects of within-neuron degree correlations in networks of spiking neurons
• The effects of degree distributions in random networks of Type-I neurons