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dc.contributor.advisorVan Vleck, Erik S
dc.contributor.authorLamb, Charles
dc.date.accessioned2013-02-17T16:43:08Z
dc.date.available2013-02-17T16:43:08Z
dc.date.issued2012-12-31
dc.date.submitted2012
dc.identifier.otherhttp://dissertations.umi.com/ku:12390
dc.identifier.urihttp://hdl.handle.net/1808/10819
dc.description.abstractIn this dissertation we consider neutral equations of mixed type. In particular, we con- sider the associated linear Fredholm theory and nerve fiber models that are written as systems of neutral equations of mixed type. In Chapter 2, we extend the existing Fredholm theory for mixed type functional differential equations developed by Mallet-Paret to the case of implicitly defined mixed type functional differential equations. In Chapter 3, we apply the theory to an example arising from modeling signal prop- agation in nerve fibers. In this two-dimensional system, we rely on the Lyapunov- Schmidt method to demonstrate the existence of traveling wave solutions. With the aid of numerical computations, a saddle-node bifurcation was detected. In Chapter 4, we consider an extension of the parallel nerve fiber model examining in Chapter 3 and present the results of a numerical study. In this chapter, an additional form of coupling is examined not considered in the model from Chapter 3. This second type of coupling may be excitatory or inhibitory depending on the sign of the coupling parameter. Within a continuation framework, we employ a pseudo-spectral approach utilizing Chebyshev polynomials as basis functions. The chebfun package, consisting of Chebyshev tools, was utilized to manipulate the polynomials.
dc.format.extent127 pages
dc.language.isoen
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.subjectFunctional differential equations
dc.subjectLyapunov-schmidt
dc.subjectNeutral equations
dc.titleNeutral Equations of Mixed Type
dc.typeDissertation
dc.contributor.cmtememberHuang, Weizhang
dc.contributor.cmtememberLiu, Weishi
dc.contributor.cmtememberStefanov, Atanas
dc.contributor.cmtememberChertoff, Mark
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelPh.D.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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