Singularly perturbed boundary-focus bifurcations
DOI10.1016/j.jde.2021.06.008zbMath1472.34109arXiv2006.06087OpenAlexW3170826637MaRDI QIDQ2040129
Samuel Jelbart, K. Uldall Kristiansen, Martin Wechselberger
Publication date: 12 July 2021
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.06087
non-smooth systemssingular perturbationsblow-upregularisationrelaxation oscillationsnon-smooth bifurcations
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)
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Cites Work
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- Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems
- Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle
- Neural excitability and singular bifurcations
- Piecewise smooth dynamical systems theory: the case of the missing boundary equilibrium bifurcations
- Multiple time scale dynamics
- Slow-fast Bogdanov-Takens bifurcations
- Generic bifurcations of planar Filippov systems via geometric singular perturbations
- A singular approach to discontinuous vector fields on the plane
- Analytical approximations for stick-slip vibration amplitudes
- Birth of canard cycles
- Geometric singular perturbation analysis of an autocatalator model
- Geometric singular perturbation theory for ordinary differential equations
- Functional equations and conjugacy of local diffeomorphisms of a finite smoothness class
- Canonical forms for codimension one planar piecewise smooth vector fields with sliding region
- Global dynamics of a mechanical system with dry friction
- The regularized visible fold revisited
- Singular systems on the plane and in space
- Geometric singular perturbation analysis of a dynamical target mediated drug disposition model
- Piecewise-smooth dynamical systems. Theory and applications
- Resolution of the piecewise smooth visible-invisible two-fold singularity in \(\mathbb {R}^3\) using regularization and blowup
- Sliding vector fields via slow-fast systems
- Regularization of discontinuous vector fields on \({\mathbb{R}^3}\) via singular perturbation
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Classification of Hidden Dynamics in Discontinuous Dynamical Systems
- Regularizations of Two-Fold Bifurcations in Planar Piecewise Smooth Systems Using Blowup
- Stick-slip vibrations and chaos
- Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation
- One-Parameter Bifurcations in Planar Filippov Systems
- Canard cycles and center manifolds
- Hidden Dynamics
- Singular limit analysis of a model for earthquake faulting
- Two-stroke relaxation oscillators
- A new type of relaxation oscillation in a model with rate-and-state friction
- Geometric Singular Perturbation Theory Beyond the Standard Form
- On the Use of Blowup to Study Regularizations of Singularities of Piecewise Smooth Dynamical Systems in $\mathbb{R}^3$
- Blowup for flat slow manifolds
- Scaling in Singular Perturbation Problems: Blowing Up a Relaxation Oscillator
- Two Degenerate Boundary Equilibrium Bifurcations in Planar Filippov Systems
- Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit
- Elements of applied bifurcation theory
- Relaxation oscillation and canard explosion
- On the Gause predator-prey model with a refuge: a fresh look at the history
