Title |
Stochastic Hybrid Systems in Cellular Neuroscience
|
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Published in |
The Journal of Mathematical Neuroscience, August 2018
|
DOI | 10.1186/s13408-018-0067-7 |
Pubmed ID | |
Authors |
Paul C. Bressloff, James N. Maclaurin |
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. |
Mendeley readers
Geographical breakdown
Country | Count | As % |
---|---|---|
Unknown | 26 | 100% |
Demographic breakdown
Readers by professional status | Count | As % |
---|---|---|
Researcher | 9 | 35% |
Student > Ph. D. Student | 7 | 27% |
Student > Bachelor | 2 | 8% |
Other | 1 | 4% |
Lecturer | 1 | 4% |
Other | 3 | 12% |
Unknown | 3 | 12% |
Readers by discipline | Count | As % |
---|---|---|
Mathematics | 8 | 31% |
Neuroscience | 4 | 15% |
Physics and Astronomy | 3 | 12% |
Engineering | 2 | 8% |
Agricultural and Biological Sciences | 1 | 4% |
Other | 2 | 8% |
Unknown | 6 | 23% |