Abstract
In this paper, the stability analysis of the neural field model is studied. The special case for three neuron populations is considered. The work is conducted by finding the characteristic equation of the system first and then investigating the characteristic roots of the third-order equation by using the Routh-Hurwitz criterion and Sturm sequence. The main analysis is given in two parts considering the nonexistence and existence of the delay term. Some basic stability criteria in terms of coefficients of the system are given in the theorems.
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