A synaptic model for the kindling effect

In this work we present a model of the kindling effect based on the Hopf bifurcation for a system of ordinary differential equations. The model shows how quantitative changes in the physiological parameters at the microscopic, synaptic scale, produce the afterdischarge which is a macroscopic effect at the neuronal network scale. The presynaptic mechanisms are based on the vesicular hypothesis, or more generally on the quantal theory of synaptic transmission. The postsynaptic processes rely on Granit's law. This model gives a consistent framework which organizes and explains several experimental observations.