Stochastic Dynamics of some Neuron Models

Priscilla Greenwood (September 16, 2011)

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Abstract

How does a stochastic process move between the domains of attraction of locally stable points or cycles of an associated deterministic system, and cross unstable cycles? This question arises when we try to quantify the behavior of a neuron in terms of a stochastic neuron model. In the Morris Lecar model, for instance, the much-studied interspike-interval distribution depends on a process exiting from a quasi-stationary state near a fixed point and crossing an unstable limit cycle. When a process encounters an unstable cycle it tends to follow along a bit. But we need to do better than that.

References:

* P Baxendale and P E Greenwood, Sustained oscillations for density dependent Markov processes. J. Math Biology, Sept 2011.
* S Ditlevsen and P E Greenwood, (2011) The Morris-Lecar neuron model embeds a leaky integrate-and-fire model, arXiv 1108.0073.
* P F Rowat and P E Greenwood, Identification and continuity of the distributions of burst length and inter-spike intervals in the stochastic Morris Lecar neuron. Neural Computation, to appear.