Bifurcations in a Delay Logistic Equation Under Small Perturbations

In this paper, we consider dynamic properties of a delay logistic equation. In the first section, by using bifurcation methods we study the local behavior of solutions to the initial equation. We pay the main attention to studying the dependence of dynamic properties of solutions on small perturbations with a large delay. We construct special nonlinear parabolic-type equations, whose local dynamics describes the behavior of solutions in a small neighborhood of the equilibrium state of the initial equation with delay. In the second section, with the help of asymptotic methods we study an important for applications issue related to the parametric resonance under a two-frequency perturbation.