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

"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."

Model Type: Neuron or other electrically excitable cell

Cell Type(s): Pituitary cell

Currents: I A; I K; I K,Ca; I Calcium

Model Concept(s): Bursting; Oscillations; Bifurcation

Simulation Environment: XPP (web link to model)


Teka W, Tabak J, Bertram R. (2012). The relationship between two fast/slow analysis techniques for bursting oscillations. Chaos (Woodbury, N.Y.). 22 [PubMed]

This website requires cookies and limited processing of your personal data in order to function. By continuing to browse or otherwise use this site, you are agreeing to this use. See our Privacy policy and how to cite and terms of use.