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yxp30-thesis.pdf (633.97 KB)
ETD Abstract Container
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Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems
Author Info
Park, Youngmin
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724
Abstract Details
Year and Degree
2013, Master of Sciences, Case Western Reserve University, Applied Mathematics.
Abstract
Dynamical systems with discontinuous right-hand sides are utilized to great effect in mathematical biology (Coombes 2008, Glass and Kauffman 1973, McKean 1970), including models of central pattern generators (CPGs) involved in motor control (Spardy et al. 2011, Shaw et al. 2012). CPG models typically exhibit limit cycle dynamics; the infinitesimal phase response curve (iPRC) quantifies sensitivity of such models to external inputs (Ermentrout and Terman 2010). Piecewise smooth dynamical systems may have discontinuous iPRCs. In this thesis, we formulate the boundary conditions necessary for obtaining the iPRC for general piecewise smooth dynamical systems by solving an adjoint equation, thereby improving upon two known methods used to solve for the iPRC in the context of piecewise linear dynamical systems.
Committee
Peter Thomas, PhD (Committee Chair)
Hillel Chiel, PhD (Committee Co-Chair)
Alethea Barbaro, PhD (Committee Member)
Michael Hurley, PhD (Committee Member)
Pages
69 p.
Subject Headings
Applied Mathematics
;
Biomechanics
;
Mathematics
;
Neurosciences
Keywords
Phase response curve
;
piecewise smooth dynamical systems
;
piecewise linear dynamical systems
;
adjoint equation
;
central pattern generator
;
motor control
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Citations
Park, Y. (2013).
Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems
[Master's thesis, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724
APA Style (7th edition)
Park, Youngmin.
Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems.
2013. Case Western Reserve University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724.
MLA Style (8th edition)
Park, Youngmin. "Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems." Master's thesis, Case Western Reserve University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724
Chicago Manual of Style (17th edition)
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Document number:
case1370643724
Download Count:
695
Copyright Info
© 2013, some rights reserved.
Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems by Youngmin Park is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.