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<T1), is unstable for T1<T<T2, and regains its stability for large delays T>T2. We show that for T1<T<T2 a stable oscillatory state, exists which bifurcates from the equilibrium state through an exchange of stability at T=T1 and T=T2. Numerical computations and graphs of the solutions are given for the solutions in all ranges of T. © 1979.