"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."
Reference:
1 .
Teka W, Tabak J, Bertram R (2012) The relationship between two fast/slow analysis techniques for bursting oscillations. Chaos 22:043117 [PubMed]
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