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 equationandabout their equilibrium points. Also we study the stability of these equilibrium points and prove that every non-oscillatory positive solution tends to the equilibrium point when t tends to infinity. Where Eq (*) proposed by Mackey and Glass [12] for a “Dynamic Disease” involving respiratory disorders and Eq. (**) is one of the models proposed by Nazarenko [13] to study a control of a single population of cells