Bifurcations in a delay logistic equation under small perturbations

The article considers the dynamic properties of a logistic equation with delay. The first section studies the local behavior of the original equation solutions with the help of bifurcational methods. The main attention is paid to the question of the influence of small perturbations with large delay on the dynamic properties of the solutions. Special nonlinear equations of the parabolic type are constructed. Their local dynamics describes the behavior of the solutions from the small neighborhood of the balance state for the original equation with delay. The second section studies the important for applications question of a parametric resonance at two-frequency disturbance with the help of asymptotic methods.