Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling

Abstract

We derive the Kuramoto model (KM) corresponding to a population of weakly coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both electrical and chemical coupling. The ratio of chemical to electrical coupling determines the phase lag of the characteristic sine coupling function of the KM and critically determines the synchronization properties of the network. We apply our results to investigate chimera states in two coupled populations of identical QIF neurons. We find that the presence of both electrical and chemical coupling is a necessary condition for chimera states to exist. Finally, we numerically demonstrate that chimera states gradually disappear as coupling strengths cease to be weak.

References in corpus (37)

• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Solvable model for chimera states of coupled oscillators
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• When Nonlocal Coupling Between Oscillators Becomes Stronger: Patched Synchrony or Multi-Chimera States
• The physics of brain network structure, function, and control
• Macroscopic description for networks of spiking neurons
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• Partially integrable dynamics of hierarchical populations of coupled oscillators
• Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Synchronization of two interacting populations of oscillators
• Chimera states in heterogeneous networks
• Chimera states in networks of nonlocally coupled Hindmarsh-Rose neuron models
• Chimera-like states in modular neural networks
• Instability of synchronized motion in nonlocally coupled neural oscillators
• Collective chaos in pulse-coupled neural networks
• Low-dimensional dynamics of populations of pulse-coupled oscillators
• FitzHugh-Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena
• Frustrated hierarchical synchronization and emergent complexity in the human connectome network
• Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks
• Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
• Chimera states in two populations with heterogeneous phase-lag
• Heterogeneity of time delays determines synchronization of coupled oscillators
• Non-universal results induced by diversity distribution in coupled excitable systems
• Exact mean-field theory explains the dual role of electrical synapses in collective synchronization
• Clustered Chimera States in Systems of Type-I Excitability
• Kuramoto model for excitation-inhibition-based oscillations
• Shear diversity prevents collective synchronization
• The changing notion of chimera states, a critical review
• An exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks
• Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case
• On the equivalence of phase-oscillator and integrate-and-fire models
• Quasi regular concentric waves in heterogeneous lattices of coupled oscillators
• First-order phase transitions in the Kuramoto model with compact bimodal frequency distributions
• The effect of noise on the synchronization dynamics of the Kuramoto model on a large human connectome graph

Cited by in corpus (7)

• Exact finite-dimensional description for networks of globally coupled spiking neurons
• Synchronization in the Kuramoto model in presence of stochastic resetting
• Pulse shape and voltage-dependent synchronization in spiking neuron networks
• Predicting the response of structurally altered and asymmetrical networks
• Metastability of multi-population Kuramoto-Sakaguchi oscillators
• Explosive synchronization in networks of Type-I neurons with electrical synapses
• Synchronization modes in bipartite oscillator networks