On perturbations of autonomous ODE systems preserving some properties of solutions

Title	On perturbations of autonomous ODE systems preserving some properties of solutions
Authors	E. V. Musafirov¹ ¹Yanka Kupala State University of Grodno
Annotation	A non-autonomous perturbation of an autonomous system of ordinary dif-ferential equations is considered, which is the right part of an autonomous system multiplied by a scalar function depending on time. It is proved that this perturbation preserves the qualitative properties of solutions of an autonomous system, such as the presence of periodic solutions and the Lyapunov stability of solutions. These results allow us to find out which perturbation will not affect the qualitative behavior of solutions when modeling real processes.
Keywords	Mironenko reflecting function, periodic solution, equilibrium point, uniform asymptotic Lyapunov stability, limit cycle
Citation	Musafirov E. V. ''On perturbations of autonomous ODE systems preserving some properties of solutions'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 175-183. Available at: https://conf.svmo.ru/files/2023/papers/paper28.pdf. - Date of access: 19.05.2024.