3D quadratic ODE systems with hidden oscillations

Abstract An autonomous three-dimensional quadratic system of ordinary differential equations with two parameters is considered. This system exhibits hidden oscillations at certain parameter values (it has a limit cycle, but does not have equilibrium points). We are looking for non-autonomous perturbations of this autonomous system that do not change the Mironenko reflecting function. Such so-called admissible perturbations preserve some qualitative properties of the solutions of the original system. For perturbed non-autonomous systems, we derived the Lyapunov stability of equilibrium solutions, proved the existence of the limit cycle and periodic solutions, as well as their stability (instability).