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.

在本文中，我们考虑了时滞逻辑方程的动力学性质。在第一部分中，通过使用分叉方法，我们研究了初始方程解的局部行为。我们主要关注研究溶液动力学特性对小扰动和大延迟的依赖性。我们构造了特殊的非线性抛物线型方程，其局部动力学描述了具有延迟的初始方程平衡状态的小邻域中解的行为。在第二部分中，借助渐近方法，我们研究了在双频扰动下与参数共振相关的应用问题的重要问题。