The Modeling of Spike-Wave Discharges in Brain with Small Oscillatory Neural Networks

A pathology of coupling architecture in the thalamo-cortical system is considered the main cause of absence epilepsy, the eletroencephalographic primary manifestation of which are spike-wave discharges. The immediate cause of the discharges may be in increase of intracortical connectivity or external stimulation of cortex or thalamus. At the same time, the mechanisms of discharge termination are still not clear; so from the point of view of the dynamical system theory, the spike-wave discharge can be considered as a long transient process. In this paper, we propose a simple mathematical model of network with 14 identical Fitzhugh–Nagumo neurons, which is organized in accordance with modern ideas about thalamo-cortical brain network. In this model, long transients in response to short-term pulse driving from a separate neuron, representing the nervus trigeminus, are shown to be possible. Bifurcation analysis reveals such transients to develop in the system approximately the bifurcation of the cycle birth from the condensation of phase trajectories. The model may be useful for detailed studies of the thalamo-cortical system. It also can be used to investigate effects of electrical brain stimulation and pharmacological interventions, and to test the methods for evaluating connectivity in brain.