À propos de canards (Apropos canards)
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Publication:2884404
DOI10.1090/S0002-9947-2012-05575-9zbMath1244.34080MaRDI QIDQ2884404
Publication date: 29 May 2012
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Singularities of vector fields, topological aspects (58K45) Invariant manifolds for ordinary differential equations (34C45) Singular perturbations for ordinary differential equations (34E15) Stability of manifolds of solutions to ordinary differential equations (34D35) Canard solutions to ordinary differential equations (34E17)
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Cites Work
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- Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics
- The canard unchained or how fast/slow dynamical systems bifurcate
- Bifurcations of mixed-mode oscillations in a stellate cell model
- Local analysis near a folded saddle-node singularity
- The geometry of mixed-mode oscillations in the Olsen model for the peroxidase-oxidase reaction
- Homoclinic clusters and chaos associated with a folded node in a stellate cell model
- Applications of centre manifold theory
- Geometric singular perturbation theory for ordinary differential equations
- Differential equations with small parameters and relaxation oscillations. Translation from the Russian by F. M. C. Goodspeed
- Duck-shaped solutions and winding.
- Relaxation oscillations in \({\mathbb R}^3\)
- Nonstandard analysis in practice
- Geometric desingularization of a cusp singularity in slow-fast systems with applications to Zeeman's examples
- Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model
- Mixed mode oscillations as a mechanism for pseudo-plateau bursting
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Mixed-Mode Oscillations with Multiple Time Scales
- Numerical continuation of canard orbits in slow–fast dynamical systems
- Folds, canards and shocks in advection–reaction–diffusion models
- Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
- The Geometry of Slow Manifolds near a Folded Node
- Singular Hopf Bifurcation in Systems with Two Slow Variables
- Canard Induced Mixed-Mode Oscillations in a Medial Entorhinal Cortex Layer II Stellate Cell Model
- Canards, Clusters, and Synchronization in a Weakly Coupled Interneuron Model
- Delay induced canards in a model of high speed machining
- Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
- Relaxation oscillations including a standard chase on French ducks
- Extending Melnikov theory to invariant manifolds on non-compact domains
- Analysis of a Canard Mechanism by Which Excitatory Synaptic Coupling Can Synchronize Neurons at Low Firing Frequencies
- Canard cycles and center manifolds
- Geometry of Mixed-Mode Oscillations in the 3-D Autocatalator
- The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales
- Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron
- Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system
- Understanding anomalous delays in a model of intracellular calcium dynamics
- Invariant manifolds
- Relaxation oscillation and canard explosion
- Canards in \(\mathbb{R}^3\)