Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons

Abstract

We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of non-symmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, also chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.

References in corpus (5)

• Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
• Macroscopic description for networks of spiking neurons
• Robustness of chimera states for coupled FitzHugh-Nagumo oscillators
• Instability of synchronized motion in nonlocally coupled neural oscillators
• Chimera states on the surface of a sphere

Cited by in corpus (8)

• Population spiking and bursting in next generation neural masses with spike-frequency adaptation
• Mean-field equations for neural populations with $q$-Gaussian heterogeneities
• Effect of Cauchy noise on a network of quadratic integrate-and-fire neurons with non-Cauchy heterogeneities
• Suppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons
• Dynamics of a network of quadratic integrate-and-fire neurons with bimodal heterogeneity
• Control of seizure-like dynamics in neuronal populations with excitability adaptation related to ketogenic diet
• Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons
• Chimeras with uniformly distributed heterogeneity: two coupled populations