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Markov Jump Process Ion Channel Models

Wednesday, May 15, 2013 - 10:15am - 11:05am
Keller 3-180
Peter Thomas (Case Western Reserve University)
In deterministic dynamics, a stable limit cycle is a closed, isolated
periodic orbit that attracts nearby trajectories. Points in its basin of
attraction may be disambiguated by their asympototic phase. In
stochastic systems with approximately periodic trajectories, asymptotic
phase is no longer well defined, because all initial densities converge
to the same stationary measure. We explore circumstances under which one
may nevertheless define an analog of the asymptotic phase. In
particular, we consider jump Markov process models incorporating ion
channel noise, and study a stochastic version of the classical
Morris-Lecar system in this framework. We show that the stochastic
asymptotic phase can be defined even for some systems in which no
underlying deterministic limit cycle exists, such as an attracting
heteroclinic cycle perturbed by additive noise. We also discuss an
analysis of an efficient numerical approximation for simulating
trajectories of randomly gated ion channels, called the stochastic
shielding approximation, recently introduced by Schmandt and Galan
(Physical Review Letters, 2012).
MSC Code: 
60J75