On the dynamics of bursting systems
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Publication:2641238
DOI10.1007/BF00160469zbMath0721.92004WikidataQ52462594 ScholiaQ52462594MaRDI QIDQ2641238
James C. Alexander, Da-Yong Cai
Publication date: 1991
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
attractorBifurcationfast-slow decompositiondynamics of three- variable models of burstinglogistic interval mappancreatic beta-cell model
Probabilistic models, generic numerical methods in probability and statistics (65C20) Physiology (general) (92C30) Physiological, cellular and medical topics (92C99) Dynamical systems and ergodic theory (37-XX)
Related Items (13)
Understanding bursting oscillations as periodic slow passages through bifurcation and limit points ⋮ The transition from bursting to continuous spiking in excitable membrane models ⋮ Full system bifurcation analysis of endocrine bursting models ⋮ Singularities of equations of Hodgkin–Huxley type ⋮ Mathematical perspective of Hodgkin-Huxley model and bifurcation analysis ⋮ Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation ⋮ Reduction of a model of an excitable cell to a one-dimensional map ⋮ NEURAL EXCITABILITY, SPIKING AND BURSTING ⋮ Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos ⋮ Uniqueness and stability of periodic bursting solutions ⋮ Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle ⋮ Dynamics of the calcium subsystem in cardiac Purkinje fibers ⋮ Mixed-mode oscillation genealogy in a compartmental model of bone mineral metabolism
Uses Software
Cites Work
- Coupling of a slow and a fast oscillator can generate bursting
- Qualitative study of a dynamical system for metrazol-induced paroxysmal depolarization shifts
- Chaos in a three-variable model of an excitable cell
- An analysis of a dendritic neuron model with an active membrane site
- Dissection of a model for neuronal parabolic bursting
- Qualitative analysis of a model generating long potential waves in Ba- treated nerve cells. II. Complete system
- Bifurcation and resonance in a model for bursting nerve cells
- Qualitative analysis of a model generating long potential waves in Ba- treated nerve cells. I. Reduced systems
- A one-variable map analysis of bursting in the Belousov-Zhabotinskiĭ reaction
- Parabolic Bursting in an Excitable System Coupled with a Slow Oscillation
- On the Resonance Structure in a Forced Excitable System
- Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
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