Linear Stability Analysis of a Delay Differential Equation

In this paper, a delay differential equations deduced from mathematical biology is considered. The linear stability of the steady states of these types of equations is one of the main problem in this theory. This is harder than usual differential equations because of their infinite dimensional nature. In this essay, we use a method to reduce the question of missing of stability due to existence of time delay, to the problem of finding real positive roots of a polynomial