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|Title: ||Bifurcation analysis of a system of Morris-Lecar neurons with time delayed gap junctional coupling|
|Authors: ||Kobelevskiy, Ilya|
|Keywords: ||invariant manifold reduction|
nearly linear systems
gap junctional coupling
delay differential equations
|Approved Date: ||27-Aug-2008 |
|Date Submitted: ||2008 |
|Abstract: ||We consider a system of two identical Morris-Lecar neurons coupled via electrical coupling. We focus our study on the effects that the coupling strength, γ , and the coupling time delay, τ , cause on the dynamics of the system.
For small γ we use the phase model reduction technique to analyze the system behavior. We determine the stable states of the system with respect to γ and τ using the appropriate phase models, and we estimate the regions of validity of the phase models in the γ , τ plane using both analytical and numerical analysis.
Next we examine asymptotic of the arbitrary conductance-based neuronal model for γ → +∞ and γ → −∞. The theory of nearly linear systems developed in  is extended in the special case of matrices with non-positive eigenvalues. The asymptotic analysis for γ > 0 shows that with appropriate choice of γ the voltages of the neurons can be made arbitrarily close in finite time and will remain that close for all subsequent time, while the asymptotic analysis for γ < 0 suggests the method of estimation of the boundary between “weak” and “strong” coupling.|
|Program: ||Applied Mathematics|
|Department: ||Applied Mathematics|
|Degree: ||Master of Mathematics|
|Appears in Collections:||Electronic Theses and Dissertations (UW)|
Faculty of Mathematics Theses and Dissertations
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