The relationship between two fast/slow analysis techniques for bursting oscill. (Teka et al. 2012)

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"Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical manifold. … We find that the z-curve and Hopf bifurcation of the twofast/ one-slow decomposition are closely related to the voltage nullcline and folded node singularity of the one-fast/two-slow decomposition, respectively. They become identical in the double singular limit in which voltage is infinitely fast and calcium is infinitely slow."
1 . Teka W, Tabak J, Bertram R (2012) The relationship between two fast-slow analysis techniques for bursting oscillations. Chaos 22:043117 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Pituitary cell;
Channel(s): I A; I K; I K,Ca; I Calcium;
Gap Junctions:
Simulation Environment: XPP (web link to model);
Model Concept(s): Bursting; Oscillations; Bifurcation;
Search NeuronDB for information about:  I A; I K; I K,Ca; I Calcium;
(located via links below)
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