Regularization and Geometry of Piecewise Smooth Systems with Intersecting Discontinuity Sets

DOI10.1137/18M1214470zbMath1431.37046arXiv1909.09810OpenAlexW2955508785WikidataQ127597128 ScholiaQ127597128MaRDI QIDQ5238230

Panagiotis Kaklamanos, K. Uldall Kristiansen

Publication date: 28 October 2019

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.09810

zbMATH Keywords

regularizationblowuppiecewise smooth systemssingular perturbation theoryintersecting discontinuity sets

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Computational methods for bifurcation problems in dynamical systems (37M20) Singular perturbations for ordinary differential equations (34E15) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Related Items (8)

Piecewise holomorphic systems ⋮ Trajectory sensitivity analysis of hybrid systems with sliding motion ⋮ Bifurcations of the limit directions in extended Filippov systems ⋮ On Differential Equations with Codimension-$n$ Discontinuity Sets ⋮ The regularized visible fold revisited ⋮ Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit ⋮ Regularization of Isolated Codimension-2 Discontinuity Sets ⋮ An efficient algorithm for solving piecewise-smooth dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems
• Multiple time scale dynamics
• The moments sliding vector field on the intersection of two manifolds
• Geometric singular perturbation theory for ordinary differential equations
• Solutions leaving a codimension-\(2\) sliding
• Regularizing piecewise smooth differential systems: co-dimension 2 discontinuity surface
• Piecewise-smooth dynamical systems. Theory and applications
• Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field
• Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Extending slow manifolds near transcritical and pitchfork singularities
• Dynamics at a Switching Intersection: Hierarchy, Isonomy, and Multiple Sliding
• The Geometry of Generic Sliding Bifurcations
• Classification of Hidden Dynamics in Discontinuous Dynamical Systems
• Regularizations of Two-Fold Bifurcations in Planar Piecewise Smooth Systems Using Blowup
• Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation
• The Two-Fold Singularity of Discontinuous Vector Fields
• On the Use of Blowup to Study Regularizations of Singularities of Piecewise Smooth Dynamical Systems in $\mathbb{R}^3$
• Blowup for flat slow manifolds
• Relaxation oscillation and canard explosion
• Canards in \(\mathbb{R}^3\)

This page was built for publication: Regularization and Geometry of Piecewise Smooth Systems with Intersecting Discontinuity Sets