Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles
Douglas D Novaes, Gabriel Rondón
Abstract
Abstract Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization of Filippov systems. In this paper, we are interested in C n -regularizations of Filippov systems around visible regular-tangential singularities of even multiplicity. More specifically, using Fenichel theory and blow-up methods, we aim to understand how the trajectories of the regularized system transits through the region of regularization. We apply our results to investigate C n -regularizations of boundary limit cycles with even multiplicity contact with the switching manifold.
Topics & Concepts
Gravitational singularityMathematicsSmoothingLimit (mathematics)Mathematical analysisRegularization (linguistics)Boundary value problemSingularityBoundary (topology)Multiplicity (mathematics)Applied mathematicsDifferential inclusionLimit cycleDifferential equationSingularity theoryAdvanced Differential Equations and Dynamical SystemsStability and Control of Uncertain SystemsControl and Dynamics of Mobile Robots