Canards of Folded Saddle-Node Type I
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Publication:2943507
DOI10.1137/140965818zbMath1325.34071OpenAlexW1204777979MaRDI QIDQ2943507
Martin Wechselberger, Theodore Vo
Publication date: 3 September 2015
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140965818
Bifurcation theory for ordinary differential equations (34C23) Invariant manifolds for ordinary differential equations (34C45) Singular perturbations for ordinary differential equations (34E15) Canard solutions to ordinary differential equations (34E17)
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Cites Work
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- Bifurcations of canard-induced mixed mode oscillations in a pituitary lactotroph model
- Slow passage through canard explosion and mixed-mode oscillations in the forced Van der Pol's equation
- Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics
- The canard unchained or how fast/slow dynamical systems bifurcate
- Local analysis near a folded saddle-node singularity
- On stability loss delay for dynamical bifurcations
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- 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.
- Singular Hopf bifurcation in systems with fast and slow variables
- Canards in a surface oxidation reaction
- Relaxation oscillations in \({\mathbb R}^3\)
- Nonstandard analysis in practice
- The dynamics underlying pseudo-plateau bursting in a pituitary cell model
- Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Extending slow manifolds near transcritical and pitchfork singularities
- Multiple Geometric Viewpoints of Mixed Mode Dynamics Associated with Pseudo-plateau Bursting
- À propos de canards (Apropos canards)
- Mixed-Mode Oscillations with Multiple Time Scales
- Folded Saddles and Faux Canards
- Numerical continuation of canard orbits in slow–fast dynamical systems
- 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
- Singular Hopf Bifurcation to Relaxation Oscillations. II
- The Forced van der Pol Equation II: Canards in the Reduced System
- Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
- The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
- Singular Hopf Bifurcation to Relaxation Oscillations
- The Slow Passage through a Hopf Bifurcation: Delay, Memory Effects, and Resonance
- 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 and slow manifolds in the self-coupled FitzHugh-Nagumo system
- Understanding anomalous delays in a model of intracellular calcium dynamics
- Interaction of Canard and Singular Hopf Mechanisms in a Neural Model
- Canard Theory and Excitability
- Relaxation oscillation and canard explosion
- Canards in \(\mathbb{R}^3\)