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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…
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…