Bifurcations of mixed-mode oscillations in a stellate cell model
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Publication:843008
DOI10.1016/j.physd.2009.04.017zbMath1177.37086OpenAlexW2034000555MaRDI QIDQ843008
Martin Wechselberger, Warren Weckesser
Publication date: 28 September 2009
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2009.04.017
Dynamical systems in biology (37N25) Biophysics (92C05) Cell biology (92C37) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
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Uses Software
Cites Work
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- Local analysis near a folded saddle-node singularity
- Homoclinic clusters and chaos associated with a folded node in a stellate cell model
- Geometric singular perturbation theory for ordinary differential equations
- Relaxation oscillations in \({\mathbb R}^3\)
- 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
- 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
- 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
- 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
- Relaxation oscillation and canard explosion
- Canards in \(\mathbb{R}^3\)
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