Canard-like phenomena in piecewise-smooth Van der Pol systems

DOI10.1063/1.4885502zbMath1345.34070arXiv1311.5192OpenAlexW1972486263WikidataQ51071133 ScholiaQ51071133MaRDI QIDQ2821569

No author found.

Publication date: 21 September 2016

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

Full work available at URL: https://arxiv.org/abs/1311.5192

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (14)

The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations ⋮ Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ Dimension reduction for slow-fast, piecewise-linear ODEs and obstacles to a general theory ⋮ Smooth to discontinuous systems: a geometric and numerical method for slow-fast dynamics ⋮ Super-explosion and inverse canard explosion in a piecewise-smooth slow-fast Leslie-Gower model ⋮ Two-fold singularities in nonsmooth dynamics—Higher dimensional analogs ⋮ Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line ⋮ Relaxation oscillations and canard explosion in a predator-prey system of Holling and Leslie types ⋮ Fractal dimensions and two-dimensional slow-fast systems ⋮ Canard Explosion and Relaxation Oscillation in Planar, Piecewise-Smooth, Continuous Systems ⋮ Canard explosion, homoclinic and heteroclinic orbits in singularly perturbed generalist predator–prey systems ⋮ Canards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems ⋮ Duck traps: two-dimensional critical manifolds in planar systems ⋮ Loss of Determinacy at Small Scales, with Application to Multiple Timescale and Nonsmooth Dynamics

Cites Work

• Unnamed Item
• Canard trajectories in 3D piecewise linear systems
• Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows
• Chasse au canard
• Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
• Canards in piecewise-linear systems: explosions and super-explosions
• Mixed-Mode Oscillations with Multiple Time Scales
• Stability, Instability and Chaos
• Relaxation oscillations including a standard chase on French ducks
• Canard cycles and center manifolds
• Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems
• Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHugh–Nagumo Type
• Relaxation oscillation and canard explosion

This page was built for publication: Canard-like phenomena in piecewise-smooth Van der Pol systems