BIFURCATION, BURSTING AND SPIKE GENERATION IN A NEURAL MODEL

DOI10.1142/S021812740200542XzbMath1043.37057OpenAlexW2053663078MaRDI QIDQ4736259

Willy Govaerts, Annick Dhooge

Publication date: 9 August 2004

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021812740200542x

zbMATH Keywords

periodic orbitshomoclinic orbitburstingnumerical simulationdynamical behaviourbifurcation islandPlant model

Mathematics Subject Classification ID

Neural biology (92C20) Dynamical systems in biology (37N25) Simulation of dynamical systems (37M05)

Related Items (9)

GWN-INDUCED BURSTING, SPIKING, AND RANDOM SUBTHRESHOLD IMPULSING OSCILLATION BEFORE HOPF BIFURCATIONS IN THE CHAY MODEL ⋮ Continuation-Based Numerical Detection of After-Depolarization and Spike-Adding Thresholds ⋮ Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model ⋮ Spike-adding structure in fold/hom bursters ⋮ Multiple-S-Shaped Critical Manifold and Jump Phenomena in Low Frequency Forced Vibration with Amplitude Modulation ⋮ Homoclinic organization in the Hindmarsh–Rose model: A three parameter study ⋮ Dynamical systems analysis of spike-adding mechanisms in transient bursts ⋮ Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model ⋮ Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells

Uses Software

• CONTENT
• AUTO

Cites Work

• Dissection of a model for neuronal parabolic bursting
• Bifurcation and resonance in a model for bursting nerve cells
• Topological and phenomenological classification of bursting oscillations
• Bifurcation, bursting, and spike frequency adaptation
• Computing periodic orbits with high accuracy
• Synchronization of Elliptic Bursters
• Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
• Transitions to chaos in two-dimensional double-diffusive convection
• On the Resonance Structure in a Forced Excitable System
• Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
• Nonlinear Numerics
• NEURAL EXCITABILITY, SPIKING AND BURSTING
• Death of period-doublings: Locating the homoclinic-doubling cascade

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