Classification of boundary equilibrium bifurcations in planar Filippov systems

DOI10.1063/1.4940017zbMath1390.37083OpenAlexW1207183654WikidataQ47900474 ScholiaQ47900474MaRDI QIDQ4563829

Paul Glendinning

Publication date: 4 June 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: http://eprints.maths.manchester.ac.uk/2327/1/glendinningclassvabs.pdf

zbMATH Keywords

classificationbifurcationsplanar system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Stability of solutions to ordinary differential equations (34D20) Normal forms for dynamical systems (37G05) Bifurcations of singular points in dynamical systems (37G10)

Related Items (12)

The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations ⋮ Periods 1 + 2 imply chaos in steep or nonsmooth maps ⋮ Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ A general framework for boundary equilibrium bifurcations of Filippov systems ⋮ Linearization and perturbations of piecewise smooth vector fields with a boundary equilibrium ⋮ A Locust Phase Change Model with Multiple Switching States and Random Perturbation ⋮ Two-parameter boundary equilibrium bifurcations in 3D-Filippov systems ⋮ Bifurcations of Finite-Time Stable Limit Cycles from Focus Boundary Equilibria in Impacting Systems, Filippov Systems, and Sweeping Processes ⋮ Dynamics analysis of a Filippov pest control model with time delay ⋮ Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations ⋮ Hopf-like boundary equilibrium bifurcations involving two foci in Filippov systems ⋮ Bifurcation analysis of 3D-PWS systems with two transversal switching boundaries: a case study in power electronics

Cites Work

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• Piecewise smooth dynamical systems theory: the case of the missing boundary equilibrium bifurcations
• Generic bifurcations of low codimension of planar Filippov systems
• Bifurcations of equilibria in non-smooth continuous systems
• Border-collision bifurcations including ``period two to period three for piecewise smooth systems
• Piecewise-smooth dynamical systems. Theory and applications
• Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields
• NONHYPERBOLIC BOUNDARY EQUILIBRIUM BIFURCATIONS IN PLANAR FILIPPOV SYSTEMS: A CASE STUDY APPROACH
• One-Parameter Bifurcations in Planar Filippov Systems
• Two Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systems
• Elements of applied bifurcation theory

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