Journal
PHYSICAL REVIEW E
Volume 96, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.96.042212
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- Research Council of Lithuania [S-MIP-17-55]
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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 nonsymmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, and 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.
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