The Winfree model with heterogeneous phase-response curves: Analytical results
arXiv:1809.09456 · doi:10.1088/1751-8121/ab0b4c
Abstract
We study an extension of the Winfree model of coupled phase oscillators in which both natural frequencies and phase-response curves (PRCs) are heterogeneous. In the first part of the paper we resort to averaging and derive an approximate model, in which the oscillators are coupled through their phase differences. Remarkably, this simplified model is the 'Kuramoto model with distributed shear' (2011 Phys. Rev. Lett. 106 254101). We find that above a critical level of PRC heterogeneity the incoherent state is always stable. In the second part of the paper we perform the analysis of the full model for Lorentzian heterogeneities, resorting to the Ott-Antonsen ansatz. The critical level of PRC heterogeneity obtained within the averaging approximation has a different manifestation in the full model depending on the sign of the center of the distribution of PRCs.
arXiv comment14 pages, 4 figures
References in corpus (19)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Long Time Evolution of Phase Oscillator Systems
- Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
- Low-dimensional dynamics of populations of pulse-coupled oscillators
- Comment on "Long Time Evolution of Phase Oscillator Systems" [Chaos 19,023117 (2009), arXiv:0902.2773]
- Kuramoto model for excitation-inhibition-based oscillations
- Shear diversity prevents collective synchronization
- Ott-Antonsen attractiveness for parameter-dependent oscillatory networks
- On the equivalence of phase-oscillator and integrate-and-fire models
- Robust convergence in pulse coupled oscillators with delays
- Phase diagram of a generalized Winfree model
- Synchronization of Excitatory Neurons with Strongly Heterogeneous Phase Responses
- Synchronization scenarios in the Winfree model of coupled oscillators
- Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations
- Dynamics of weakly inhomogeneous oscillator populations: Perturbation theory on top of Watanabe-Strogatz integrability
- The Kuramoto model with distributed shear
- Traces of Theta^+ pentaquark in K^+ nucleus dynamics
- Room for an S = +1 pentaquark in K^+ - nucleus phenomenology
- Synchronization hypothesis in the Winfree model