On stability of small periodic solutions (Q2202735)

The author considers normal time-periodic systems of ordinary differential equations whose right-hand smoothly depend on phase variables and small parameters. Branching conditions for small periodic solution of the system was found and the Lyapunov stability test for small solution with respect to parameters or variables are established. The Lyapunov stability test iss used for the analysis of the branching of small periodic solution. The conditions that guarantee asymptotic stability of a small periodic solution of the considered system is established in the work.