The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

DOI10.1088/1361-6544/aaaaf7zbMath1506.34057arXiv1707.08162OpenAlexW3169457090MaRDI QIDQ4569296

Iris O. Zeli, Marco Antonio Teixeira, Douglas Duarte Novaes

Publication date: 28 June 2018

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08162

zbMATH Keywords

periodic solutionsbifurcation theoryFilippov systempiecewise smooth differential systemtwo-fold singularity

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36)

Related Items

Homoclinic Boundary-Saddle Bifurcations in Planar Nonsmooth Vector Fields, Bifurcation of the critical crossing cycle in a planar piecewise smooth system with two zones, A note on Vishik's normal form, Chains in \(3D\) Filippov systems: a chaotic phenomenon, Bifurcation diagrams of global connections in Filippov systems, Stability and cyclicity of polycycles in non-smooth planar vector fields, Global dynamics and bifurcation for a discontinuous oscillator with irrational nonlinearity, Degenerate T-singularity bifurcation and crossing periodic orbits in a 3-dimensional piecewise smooth system, Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle, Algebraic Limit Cycles in Piecewise Linear Differential Systems, Degenerate grazing-sliding bifurcations in planar Filippov systems, On typical homoclinic-like loops in 3D Filippov systems, Shilnikov problem in Filippov dynamical systems, Stability conditions for refractive partially integrable piecewise smooth vector fields, Sliding Bifurcation in Planar Piecewise Smooth Systems with Two Zones Separated by an Ellipse, On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities, Bifurcations of a generalized heteroclinic loop in a planar piecewise smooth system with periodic perturbations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On resolving singularities of piecewise-smooth discontinuous vector fields via small perturbations
• On the critical crossing cycle bifurcation in planar Filippov systems
• Generic bifurcations of low codimension of planar Filippov systems
• Discontinuites de champs hamiltoniens et existence de solutions optimales en calcul des variations
• On topological stability of divergent diagrams of folds
• Generic bifurcation of sliding vector fields
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Chaos induced by sliding phenomena in Filippov systems
• The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems
• Stability conditions for discontinuous vector fields
• Introduction to differentiable manifolds.
• Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems
• Piecewise-smooth dynamical systems. Theory and applications
• Extended abstracts spring 2016. Nonsmooth dynamics. Selected papers based on the presentations at the CRM research program, Barcelona, Spain, February 1 -- April 29, 2016
• The two-fold singularity of nonsmooth flows: leading order dynamics in \(n\)-dimensions
• One-Parameter Bifurcations in Planar Filippov Systems