On the solving the second-order Verhulst differential equation with perturbed initial conditions

The article examines a dynamical system whose behavior is described by a second-order differential equation where the fundamental system of solutions consisting of functions of exponential type is replaced by bounded functions of the Verhulst model. The author investigates the question of the dependence of the behavior of a particular solution of the constructed second-order differential equation on the perturbation of its initial conditions. The general form of the perturbation is assumed to have the form of a polynomial of the second degree, depending on the auxiliary parameter $\mu$. The obtained results are illustrated by a test example with specific numerical data and corresponding graphs. The MathCAD and Wolfram Alpha software packages are used as auxiliary tools for performing calculations.