On Mitropol'skii Yu.A.'s Theorem on Periodic Solutions of Systems of Nonlinear Differential Equations with Non-Differentiable Right-Hand-Sides
The smooth second Bogolyubov's theorem is generalized for Lipschitz systems.
math.CA↗
arXiv subjects
Adriana Buica
Publications and source records attributed to Adriana Buica.
Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator
In this paper we study the existence, uniqueness and asymptotic stability of the periodic solutions for a Lipschitz system with a small right hand side. Classical hypotheses in the periodic case of second Bogolyubov's theorem imply our ones. By means of the results established we construct the curves of dependence of the amplitude of asymptotically stable $2π$--periodic solutions of the nonsmooth van der Pol oscillator on the detuning parameter and the amplitude of the perturbation. After, we compare the resonance curves obtained, with the resonance curves of the classical van der Pol oscillator which were first constructed by Andronov and Witt.
math.CA↗