Аннотация:General approach to stability study of periodic solutions is related to a classical Lyapunov’s theorem based on a linear approximation. This theorem reduces stability study of periodic solutions to stability of the system linearized at the periodic motion. Since linearized systems contain periodic coefficients the theory of parametric resonance can be applied. Such approach with the analysis of Floquet multipliers is used in [4-6]. The other traditional approach to stability study of periodic solutions is related to approximate averaging and multiple scales methods which reduce original time-dependent dynamical systems to autonomous systems. In this case stability study is reduced to analysis of fixed points.
In the present paper we study stability of periodic solutions of the harmonically excited Duffing’s equation with the direct application of the Lyapunov theorem. The damping coefficient and excitation amplitude are assumed to be small. Periodic solutions are found with the use of approximate methods. We derive the stability conditions and find stable and unstable regimes on the frequency-response curve. Two types of detuning parameter are considered and corresponding frequency-response curves are compared with the results obtained by numerical simulation.