Department of Mathematics

Intrinsic excitability and other transient effects

applied mathstransients2
Figure taken from The Journal of Mathematical Neuroscience 2: 7 (2011)

Dynamical systems tools are designed to explain the asymptotic behaviour of a system, that is, what happens after transients have died out. In many applications, however, the transients play an important role and the asymptotic behaviour is actually of little interest. For example, neurons that are excitable can produce a burst of spikes after external perturbation, even if the neuron is in its quiescent state. For the structural integrity of a building, it is important to understand what happens during an earthquake, and not only after the earthquake has stopped.

This project explores how standard tools from dynamical systems can be used to analyse transient rather than asymptotic behaviour. Of particular interest are mechanisms that induce large-amplitude oscillations. The goal is to explain geometrically how transient effects come about and use numerical tools to explore the parameter sensitivity of the observed patterns.



Researchers at The University of Auckland


Other Collaborators