Wiggly canards: growth of traveling wave trains through a family of fast-subsystem foci
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Publication:2676229
DOI10.3934/dcdss.2022036zbMath1495.34082OpenAlexW4214857547MaRDI QIDQ2676229
Paul Carter, Alan R. Champneys
Publication date: 27 September 2022
Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdss.2022036
Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Traveling wave solutions (35C07) Canard solutions to ordinary differential equations (34E17)
Uses Software
Cites Work
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- Multiple time scale dynamics
- Fast and slow waves in the FitzHugh-Nagumo equation
- Chasse au canard
- Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit
- Local and global behavior near homoclinic orbits
- Bifurcation phenomena near homoclinic systems: A two-parameter analysis
- Computational cell biology
- Spike-adding canard explosion in a class of square-wave bursters
- Mathematical physiology. I: Cellular physiology
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster
- Mixed-Mode Oscillations with Multiple Time Scales
- Fast Pulses with Oscillatory Tails in the FitzHugh--Nagumo System
- Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
- When Shil'nikov Meets Hopf in Excitable Systems
- Homoclinic orbits in the dynamics of articulated pipes conveying fluid
- Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
- ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
- Unpeeling a Homoclinic Banana in the FitzHugh--Nagumo System
- Wave train selection by invasion fronts in the FitzHugh–Nagumo equation
- Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
- Single and Multiple Pulse Waves for the FitzHugh–Nagumo
- Canard cycles and center manifolds
- Codimension-Two Homoclinic Bifurcations Underlying Spike Adding in the Hindmarsh--Rose Burster
- Pulse Replication and Accumulation of Eigenvalues
- ON THE GENERATION OF A PERIODIC MOTION FROM TRAJECTORIES DOUBLY ASYMPTOTIC TO AN EQUILIBRIUM STATE OF SADDLE TYPE
- Relaxation oscillation and canard explosion
- Canards in \(\mathbb{R}^3\)
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