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Analysis of Sleep-Wake Transition Dynamics by Stochastic Mean Field Model and Metastable State

Kim, Jung Eun
http://rave.ohiolink.edu/etdc/view?acc_num=osu1406206931

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Mathematics.
Sleep-wake dynamics change across postnatal development: wake bout durations of newborn rats are exponentially distributed but become power law distributed within three weeks, in contrast to sleep bout durations that exhibit exponential distributions at all ages. To gain insight into network processes that may underlie sleep-wake transitions in these animals, a stochastic model is constructed, consisting of two mutually-inhibitory Erdos-Renyi or scale-free random graphs in which each node represents a neuron that can be in one of three possible states (excited, basal and inhibited) with distinct firing rates. The two graphs alternate between high and low levels of activity with durations that can have either an exponential or a power law distribution depending on parameters. The dynamics are investigated by numerical and analytical studies of stochastic differential equations related to the model, including the four-dimensional stochastic mean field equations. The full model is approximated by one dimensional reflected Brownian motion which has a power law distribution of bout durations on an intermediate regime, and the approximation is supported by large deviation theory and the penalization method. \end{abstract}
Janet Best, Dr. (Advisor)
Ed Overman, Dr. (Committee Member)
David Sivakoff, Dr. (Committee Member)
129 p.
Mathematics
sleep-wake transition; stochastic mean field model; a power law distribution

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Citations

  • Kim, J. E. (2014). Analysis of Sleep-Wake Transition Dynamics by Stochastic Mean Field Model and Metastable State [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406206931

    APA Style (7th edition)

  • Kim, Jung Eun. Analysis of Sleep-Wake Transition Dynamics by Stochastic Mean Field Model and Metastable State. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1406206931.

    MLA Style (8th edition)

  • Kim, Jung Eun. "Analysis of Sleep-Wake Transition Dynamics by Stochastic Mean Field Model and Metastable State." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406206931

    Chicago Manual of Style (17th edition)

osu1406206931
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© 2014, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.