Pseudo-Hopf Bifurcation for a Class of 3D Filippov Linear Systems
José Manuel Islas, Juan Castillo, Baltazar Aguirre‐Hernández, Fernando Verduzco
Abstract
We consider a nongeneric family of 3D Filippov linear systems with a discontinuity plane that have two parallel tangency lines, such that the region between them is the sliding region. We are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles.
Topics & Concepts
MathematicsHopf bifurcationTangentLimit cycleContext (archaeology)Limit (mathematics)Biological applications of bifurcation theoryDiscontinuity (linguistics)Piecewise linear functionSaddle-node bifurcationBifurcationPlane (geometry)Class (philosophy)Dynamical systems theoryMathematical analysisNonlinear systemGeometryComputer sciencePhysicsPaleontologyQuantum mechanicsBiologyArtificial intelligenceAdvanced Differential Equations and Dynamical SystemsAdvanced Differential Geometry ResearchQuantum chaos and dynamical systems