Oscillation and stability in nonlinear delay differential equations of population dynamics

In this paper, we shall study the oscillation of all positive solutions of the nonlinear delay differential equation and about their equilibrium points. Also, we study the stability of these equilibrium points and prove that every nonoscillatory positive solution tends to the equilibrium point when t tends to infinity. Where equation (*) proposed by Mackey and Glass [1] for a “dynamic disease” involving respiratory disorders and equation (**) is one of the models proposed by Nazarenko [2] to study a control of a single population of cells.