Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle
Douglas D. Novaes, Tere M. Seara, Marco A. Teixeira, Iris O. Zeli
Abstract
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed system presents a simple twofold cycle, which is characterized by a closed trajectory connecting a visible twofold singularity to itself. It is shown that under certain generic conditions the perturbed system has sliding and crossing periodic solutions. In order to get our results, Melnikov's ideas are applied together with tools from the geometric singular perturbation theory. Finally, a study of a perturbed piecewise Hamiltonian model is performed.
Topics & Concepts
Periodic orbitsPiecewiseSingular perturbationPlanarMathematicsSingularityMathematical analysisPerturbation (astronomy)Hamiltonian systemTrajectoryQuasi periodicClass (philosophy)Periodic sequencePeriodic systemFirst orderSimple (philosophy)Dynamical systems theoryHamiltonian (control theory)Classical mechanicsPeriodic functionDifferential inclusionPhysicsMechanical systemSingularity theoryGravitational singularityPiecewise linear functionDifferential (mechanical device)Ordinary differential equationControl theory (sociology)SeparatrixFormalism (music)Advanced Differential Equations and Dynamical SystemsNonlinear Differential Equations AnalysisControl and Dynamics of Mobile Robots