Stable Oscillations in Single Species Growth Models with Hereditary Effects*

We study single species growth models incorporating hereditary effects. Detailed calculations are carried out for a specific model with one delay parameter T as T varies in the entire range T > 0. Using perturbation and bifurcation techniques, we show that the effect of the hereditary term is that the equilibrium state, which is stable for small values of T (say T< T,), is unstable for T, T2. We show that for T, <T < T2 a stable oscillatory state, exists which bifurcates from the equilibrium state through an exchange of stability at T= T, and T= T2. Numerical computations and graphs of the solutions are given for the solutions in all ranges of T.