Stochastic Hybrid Systems in Cellular Neuroscience

Paul C. Bressloff, James N. Maclaurin

Research output: Contribution to journalReview articlepeer-review

5 Scopus citations

Abstract

We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators.

Original languageEnglish (US)
Article number12
JournalJournal of Mathematical Neuroscience
Volume8
Issue number1
DOIs
StatePublished - Dec 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Neuroscience (miscellaneous)

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