32 citations · 96 across the 34 of their papers we have counts for
14 papers · 1 filter
Influence of a small perturbation on Poincare-Andronov operators with not well defined topological degree
Oleg Makarenkov
Let be the Poincare-Andronov operator over period of the -periodically perturbed autonomous system where is small. Assumi…
Domain of attraction of asymptotically stable periodic solutions obtained via averaging principle
Oleg Makarenkov
In this paper we propose an approach to evaluate the domain of attraction of asymptotically stable periodic solutions obtained via averaging principle (second Bogolubov's theorem o…
Methods of topological degree theory in Malkin I. G. - Melnikov V. K.'s problems for periodically perturbed systems
Oleg Makarenkov
A topological degree based averaging principle has been proposed by J. Mawhin in his PhD thesis [J. Mawhin, Le Probleme des Solutions Periodiques en Mecanique non Lineaire, These d…
A new approach in the theory of ordinary differential equations with small parameter
Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri
A topological degree based averaging principle has been proposed by J. Mawhin in his PhD thesis [J. Mawhin, Le Probleme des Solutions Periodiques en Mecanique non Lineaire, These d…
Small parameter perturbations of nonlinear periodic systems
Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri
In this paper we consider a class of nonlinear periodic differential systems perturbed by two nonlinear periodic terms with multiplicative different powers of a small parameter $e>…
Periodic solutions for a class of singulary perturbated systems
Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri
In this paper we provide conditions to ensure the existence, for sufficiently small, of periodic solutions of given period in a prescribed domain for a class of sin…
Poincare index and periodic solutions of perturbed autonomous systems
Oleg Makarenkov
The basic tool of classical results by Malkin and Melnikov on bifurcation of periodic solutions from nondegenerate cycles of autonomous systems with periodic perturbations is an im…
Synchronization problems for unidirectional feedback coupled nonlinear systems
O. Makarenkov, P. Nistri, D. Papini
In this paper we consider three different synchronization problems consisting in designing a nonlinear feedback unidirectional coupling term for two (possibly chaotic) dynamical sy…
Periodic bifurcation from families of periodic solutions for semilinear differential equations with Lipschitzian perturbations in Banach spaces
Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri
Let A:D(A)\to E be an infinitesimal generator either of an analytic compact semigroup or of a contractive C_0-semigroup of linear operators acting in a Banach space E. In this pape…
A continuation principle for a class of periodically perturbed autonomous systems
Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri
In this paper we evaluate the topological index of periodic solutions otained via the Malkin-Loud bifurcation result. Incidentally, we do not assume that the perturbation is differ…
Periodic solutions of periodically perturbed planar autonomous systems: A topological approach
Mikhail Kamenskii, Oleg Makarenkov, Paolo Nistri
Aim of this paper is to investigate the existence of periodic solutions of a nonlinear planar autonomous system having a limit cycle x_0 of least period T_0>0 when it is perturbed…
Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator
Adriana Buica, Jaume Llibre, Oleg Makarenkov
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…
On the rate of convergence of periodic solutions in perturbed autonomous systems as the perturbation vanishes
Oleg Makarenkov, Paolo Nistri
We consider an autonomous system in R^n having a limit cycle x_0 of period T>0 which is nondegenerate in a suitable sense. We then consider the perturbed system obtained by adding…
Periodic solutions for planar autonomous systems with nonsmooth periodic perturbations
Oleg Makarenkov, Paolo Nistri
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has on…