Nonlinear observer design and synchronization analysis for classical models of neural oscillators
Name
863159137-MIT.pdf
Description
Full printable version
Size
2.64 MB
Format
Adobe PDF
Checksum (MD5)
ab704ff06801f4d1bea680b31f8bf0e4
Author(s)
Bharath, Ranjeetha
Advisor(s)
Jean-Jacques Slotine.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
Abstract
This thesis explores four nonlinear classical models of neural oscillators, the Hodgkin- Huxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Analysis techniques for nonlinear systems were used to develop a set of observers and perform synchronization analysis on the aforementioned neural systems. By using matrix analysis techniques, a study of biological background and motivation, and MATLAB simulation with mathematical computation, it was possible to do a preliminary contraction and nonlinear control systems structural study of these classical neural oscillator models. Neural oscillation and signaling models are based fundamentally on the biological function of the neuron, with behavior mediated through the channeling of ions across a cell membrane. The variable assumed to be measured for this study is the voltage or membrane potential, which could be measured empirically through the use of a neuronal force-clamp system. All other variables were estimated by using the partial state and full state observers developed here. Preliminary observer rate convergence analysis was done for the Fitzhugh-Nagumo system, and preliminary synchronization analysis was done for both the Fitzhugh-Nagumo and the Hodgkin- Huxley systems. It was found that by using a variety of techniques and mathematical matrix analyses methods (e.g. diagonal dominance or other norms), it was possible to develop a case-by-case nonlinear control systems approach to each particular system as a biomathematical entity.
Description
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 37-38).
Subjects
Mechanical Engineering.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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