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 [30] 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.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3905 |
| Date | January 2008 |
| Creators | Kobelevskiy, Ilya |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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