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    Bursting, beating, and chaotic modes in mathematical models of the R15 cell in Aplysia

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    Author
    Canavier, Carmen Castro
    Date
    1989
    Advisor
    Clark, John W., Jr.
    Degree
    Master of Science
    Abstract
    Chaotic regimes have been observed experimentally in neurons as well as in deterministic neuronal models. The bursting R15 cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. The model of Plant and Kim is capable of exhibiting both bursting and beating modes of electrical activity. We demonstrate (1) that a chaotic regime exists between the bursting and beating modes of the model, and (2) that the model approaches chaos from both modes by a period doubling cascade. We propose an original model of R15 which differs from previous models in several ways: the inclusion of a calcium ion balance, the underlying assumption that the calcium-dependent inactivation of a calcium current rather than the calcium-dependent activation of a potassium current mediates bursting activity, and the incorporation of experimental data to the extent possible. Preliminary results support the contention that a chaotic regime is intermediate between the beating and bursting modes. (Abstract shortened with permission of author.)
    Keyword
    Neurosciences; Electronics; Electrical engineering; Biophysics; Biology; More... Engineering Less...
    Citation
    Canavier, Carmen Castro. "Bursting, beating, and chaotic modes in mathematical models of the R15 cell in Aplysia." (1989) Master’s Thesis, Rice University. https://hdl.handle.net/1911/13348.
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    • ECE Theses and Dissertations [597]
    • Rice University Electronic Theses and Dissertations [13783]

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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map