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Spike-rate adaptation and neuronal bursting in a mean-field model of brain activity. (English) Zbl 1122.92012
Summary: Spike-rate adaptation is investigated within a mean-field model of brain activity. Two different mechanisms of negative feedback are considered; one involving modulation of the mean firing threshold, and the other modulation of the mean synaptic strength. Adaptation to a constant stimulus is shown to take place for both mechanisms, and limit-cycle oscillations in the firing rate corresponding to bursts of neuronal activity are investigated. These oscillations are found to result from a Hopf bifurcation when the equilibrium lies between the local maximum and local minimum of a given nullcline. Oscillations with amplitudes significantly below the maximum firing rate are found over a narrow range of possible equilibriums.

92C20 Neural biology
45K05 Integro-partial differential equations
82D99 Applications of statistical mechanics to specific types of physical systems
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