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Dynamic Hopf Bifurcation in Spatially Extended Excitable Systems from Neuroscience


Abstract 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 significa... (more)
Created Date 2012
Contributor Bilinsky, Lydia (Author) / Baer, Steven M (Advisor) / Crook, Sharon M (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gardner, Carl L (Committee member) / Jung, Ranu (Committee member) / Arizona State University (Publisher)
Subject Applied mathematics / Neurosciences / dendritic spines / excitable systems / Hopf bifurcation / membrane accommodation
Type Doctoral Dissertation
Extent 105 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Note Ph.D. Applied Mathematics 2012
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS


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Description Dissertation/Thesis