Dynamics Of Two Population Synaptic Drive Model

Abstract

In this work we have investigated the two population synaptic drive model with a relatively complex temporal kernal for steep firing rate function. We have done this justification by deriving four dimensional autonomous dynamical system from Volterra equations using linear chain trick. Both of the local and global wellposedness of the model has been in vestigated. The existence of stationary point has also been investigated and the general formula for stationary point is derived. We get two different models for delay and non delay case. Theorem on the existence and stability has also been formulated. The stability issue has also been addressed for both cases for the steepness parameter q = 0, and q > 0, which leads us to the conclusion that delays in the system with weak kernel does not effect the stability properties of the model