|Institution:||Case Western Reserve University|
|Keywords:||Biomechanics; Applied Mathematics; Neurosciences; Mathematics; Phase response curve; piecewise smooth dynamical systems; piecewise linear dynamical systems; adjoint equation; central pattern generator; motor control|
|Full text PDF:||http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724|
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.