Understanding bursting oscillations as periodic slow passages through bifurcation and limit points

DOI10.1007/BF00163921zbMath0769.92013OpenAlexW2073808260MaRDI QIDQ2365853

Lisa Holden, Thomas Erneux

Publication date: 29 June 1993

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00163921

zbMATH Keywords

delayed bifurcationallosteric enzyme reactionslimit of large allosteric constantsslow passage through a supercritical Hopf bifurcationslowly varying oscillatory stateslowly varying steady statethree coupled, first- order nonlinear differential equationstime-periodic bursting solution

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

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Cites Work

• Coupling of a slow and a fast oscillator can generate bursting
• Dissection of a model for neuronal parabolic bursting
• On the dynamics of bursting systems
• Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions
• Slowly Varying Jump and Transition Phenomena Associated with Algebraic Bifurcation Problems
• Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
• Arrhenius Systems: Dynamics of Jump Due to Slow Passage Through Criticality
• On the Resonance Structure in a Forced Excitable System
• Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
• Perturbation Techniques for Models of Bursting Electrical Activity in Pancreatic $\beta $-Cells
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