Stochastic Hybrid Systems in Cellular Neuroscience

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.

• Publication year

  2018

• Venue

  Journal of Mathematical Neuroscience

• Publication date

  2018-08-22

• Fields of study

  Biology, Medicine, Computer Science

• Identifiers
  DOI 10.1186/s13408-018-0067-7PMID 30136005PMCID 6104574
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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