Oleg Makarenkov

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 of the Lipschitz system

Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations

\dot{x}=\varepsilon g(t,x,\varepsilon)

Small parameter perturbations of nonlinear periodic systems

, where

Poincaré index and periodic solutions of perturbed autonomous systems

\varepsilon>0

On the Behavior of Periodic Solutions of Planar Autonomous Hamiltonian Systems with Multivalued Periodic Perturbations

is small. Our results extend the classical second Bogoliubov theorem for the existence of stable periodic solutions to nonsmooth differential systems. As an application we prove the existence of asymptotically stable

Small periodic perturbations of autonomous self-oscillating planar systems

2\pi

Dynamics and bifurcations of nonsmooth systems: A survey

-periodic solutions of the nonsmooth van der Pol oscillator

A continuation principle for a class of periodically perturbed autonomoussystems

\ddot{u}+\varepsilon\,(|u|-1)\,\dot{u}+(1+a\varepsilon)u=\varepsilon\lambda\sin t

Preface: Dynamics and Bifurcations of Nonsmooth Systems

. Moreover, we construct the so-called resonance curves that describe the dependence of the amplitude of these solutions as a function of the parameters a and

An Alternative Approach to Study Bifurcation from a Limit Cycle in Periodically Perturbed Autonomous Systems

\lambda