"This dissertation focuses on several problems in neuroscience from the perspective of nonlinear dynamics and stochastic processes. The first part concerns a method to visualize the idea of the power spectrum of spike trains, which has an educational value to introductory students in biophysics. The next part consists of experimental and computational work on drug-induced epileptic seizures in the rat neocortex. In the experimental part, spatiotemporal patterns of electrical activities in the rat neocortex are measured using voltage-sensitive dye imaging. Epileptic regions show well-synchronized, in-phase activity during epileptic seizures. In the computational part, a network of a Hodgkin-Huxley type neocortical neural model is constructed. Phase reduction, which is a dimension reduction technique for a stable limit cycle, is applied to the system. The results propose a possible mechanism for the initiation of the drug-induced seizure as a result of a bifurcation. In the last part, a theoretical framework is developed to obtain the statistics for the period of oscillations of a stable limit cycle under stochastic perturbation. A stochastic version of phase reduction and first passage time analysis are utilized for this purpose. The method presented here shows a good agreement with numerical results for the weak noise regime"--Abstract, page iii.
Parris, Paul Ernest, 1954-
Feres, Renato, 1962-
Ph. D. in Physics
Epilepsy Foundation of America
National Science Foundation (U.S.)
Missouri University of Science and Technology
xii, 140 pages
© 2010 Daisuke Takeshita, All rights reserved.
Dissertation - Open Access
Nonlinear oscillations -- Testing
Epilepsy -- Pathophysiology
Epilepsy -- Animal models
Print OCLC #
Electronic OCLC #
Link to Catalog Record
Takeshita, Daisuke, "A study of synchronization of nonlinear oscillators: Application to epileptic seizures" (2010). Doctoral Dissertations. 1833.