An Analytical Study on the Synchronization of a Two-Cell Inhibitory Neural Dynamics

Biophysical observations in different brain regions have displayed synchronous firing in inhibitory neural networks. Although inhibition reduces the postsynaptic neuron’s activity, coordinated synchronous rhythms could be predicted provided that inhibition delay is incorporated into the biophysical models. In this article, we study the local dynamics of two mutually coupled neurons connected via inhibitory synapses. The key assumption in the model is that the neurotransmitter release activates some secondary synaptic processes that give additional time to the postsynaptic neuron before it feels the inhibition. Stability conditions for synchrony are derived for this simple inhibitory network. Numerical experiments are presented that justify theoretical conclusions. The geometric singular perturbation theory is used as well as a variational argument.