Monthly
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6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

August 2012, Vol. 24, No. 8, Pages 2078-2118
(doi: 10.1162/NECO_a_00308)
© 2012 Massachusetts Institute of Technology
Neural Dynamics, Bifurcations, and Firing Rates in a Quadratic Integrate-and-Fire Model with a Recovery Variable. I: Deterministic Behavior
Article PDF (2.3 MB)
Abstract

We study the dynamics of a quadratic integrate-and-fire model of a single-compartment neuron with a slow recovery variable, as input current and parameters describing timescales, recovery variable, and postspike reset change. Analysis of a codimension 2 bifurcation reveals that the domain of attraction of a stable hyperpolarized rest state interacts subtly with reset parameters, which reposition the system state after spiking. We obtain explicit approximations of instantaneous firing rates for fixed values of the recovery variable, and use the averaging theorem to obtain asymptotic firing rates as a function of current and reset parameters. Along with the different phase-plane geometries, these computations provide explicit tools for the interpretation of different spiking patterns and guide parameter selection in modeling different cortical cell types.