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

  title={Kuramoto model for populations of quadratic integrate-and-fire neurons with chemical and electrical coupling},
  author={Pau Clusella and Bastian Pietras and Ernest Montbri'o},
  journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},
with chemical and electrical coupling Pau Clusella,1 Bastian Pietras,2, 3 and Ernest Montbrió4 1)Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003, Barcelona, Spain 2)Institute of Mathematics, Technical University Berlin, 10623 Berlin, Germany. 3)Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany. 4)Neuronal Dynamics Group, Department of Information and Communication Technologies, Universitat Pompeu… 

Figures from this paper


Kuramoto Model for Excitation-Inhibition-Based Oscillations.
A two-population KM is derived that fully accounts for the onset of EI-based neuronal rhythms and is analytically solvable to a large extent, providing a powerful theoretical tool for the analysis of large-scale neuronal oscillations.
Excitatory and inhibitory interactions in localized populations of model neurons.
It is proved that the existence of limit cycle dynamics in response to one class of stimuli implies theexistence of multiple stable states and hysteresis in responseTo this work, coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons.
Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks.
  • N. Kopell, B. Ermentrout
  • Chemistry, Medicine
    Proceedings of the National Academy of Sciences of the United States of America
  • 2004
It is shown that the electrical and inhibitory coupling play different roles in the synchronization of rhythms in inhibitory networks, and that, in networks in which the degree of excitability is heterogeneous, inhibition can increase the dispersion of the voltages between spikes, whereas electrical coupling reduces such dispersion.
Gamma Oscillation by Synaptic Inhibition in a Hippocampal Interneuronal Network Model
It is demonstrated that large-scale network synchronization requires a critical (minimal) average number of synaptic contacts per cell, which is not sensitive to the network size, and that the GABAA synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons.
Emergence of chimera states in a neuronal model of delayed oscillators
Neurons are traditionally grouped in two excitability classes, which correspond to two different responses to external inputs, called phase response curves (PRCs). In this paper we have considered a
Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks.
A firing rate model is introduced that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses and agrees with several numerical studies on the dynamics of large networks of heterogeneity spiking neurons with electrical and chemical couplings.
The Dynamics of Networks of Identical Theta Neurons
  • C. Laing
  • Physics, Medicine
    Journal of mathematical neuroscience
  • 2018
It is concluded that the dynamics of networks of all-to-all coupled identical neurons can be surprisingly complicated.
Exact Neural Fields Incorporating Gap Junctions
  • C. Laing
  • Mathematics, Computer Science
    SIAM J. Appl. Dyn. Syst.
  • 2015
This work considers networks of quadratic integrate-and-fire neurons coupled via both chemical synapses and gap junctions, and performs extensive numerical analysis of the resulting equations, showing how the presence of gap junctional coupling can destroy certain spatiotemporal patterns and create others.
Equivalence of phase-oscillator and integrate-and-fire models.
  • A. Politi, M. Rosenblum
  • Mathematics, Medicine
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
It is shown that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with δ pulses and a suitable phase response curve and the regime of self-consistent partial synchronization is rather general.
Macroscopic description for networks of spiking neurons
The results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network.