Full metadata
Title
Dynamic Hopf bifurcation in spatially extended excitable systems from neuroscience
Description
One explanation for membrane accommodation in response to a slowly rising current, and the phenomenon underlying the dynamics of elliptic bursting in nerves, is the mathematical problem of dynamic Hopf bifurcation. This problem has been studied extensively for linear (deterministic and stochastic) current ramps, nonlinear ramps, and elliptic bursting. These studies primarily investigated dynamic Hopf bifurcation in space-clamped excitable cells. In this study we introduce a new phenomenon associated with dynamic Hopf bifurcation. We show that for excitable spiny cables injected at one end with a slow current ramp, the generation of oscillations may occur an order one distance away from the current injection site. The phenomenon is significant since in the model the geometric and electrical parameters, as well as the ion channels, are uniformly distributed. In addition to demonstrating the phenomenon computationally, we analyze the problem using a singular perturbation method that provides a way to predict when and where the onset will occur in response to the input stimulus. We do not see this phenomenon for excitable cables in which the ion channels are embedded in the cable membrane itself, suggesting that it is essential for the channels to be isolated in the spines.
Date Created
2012
Contributors
- Bilinsky, Lydia M (Author)
- Baer, Steven M. (Thesis advisor)
- Crook, Sharon M (Committee member)
- Jackiewicz, Zdzislaw (Committee member)
- Gardner, Carl L (Committee member)
- Jung, Ranu (Committee member)
- Arizona State University (Publisher)
Topical Subject
Resource Type
Extent
x, 94 p. : ill. (some col.)
Language
eng
Copyright Statement
In Copyright
Primary Member of
Peer-reviewed
No
Open Access
No
Handle
https://hdl.handle.net/2286/R.I.15963
Statement of Responsibility
by Lydia M. Bilinsky
Description Source
Retrieved on Oct. 8, 2013
Level of coding
full
Note
thesis
Partial requirement for: Ph.D., Arizona State University, 2012
bibliography
Includes bibliographical references (p. 85-87)
Field of study: Applied mathematics
System Created
- 2013-01-17 06:39:44
System Modified
- 2021-08-30 01:43:49
- 3 years 2 months ago
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