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Title: Multiple Time Scale Dynamics With Two Fast Variables And One Slow Variable
Authors: Kuehn, Christian
Issue Date: 5-Aug-2010
Abstract: This thesis considers dynamical systems that have multiple time scales. The focus lies on systems with two fast variables and one slow variable. The twoparameter bifurcation structure of the FitzHugh-Nagumo (FHN) equation is analyzed in detail. A singular bifurcation diagram is constructed and invariant manifolds of the problem are computed. A boundary-value approach to compute slow manifolds of saddle-type is developed. Interactions of classical invariant manifolds and slow manifolds explain the exponentially small turning of a homoclinic bifurcation curve in parameter space. Mixed-mode oscillations and maximal canards are detected in the FHN equation. An asymptotic formula to find maximal canards is proved which is based on the first Lyapunov coefficient at a singular Hopf bifurcation.
No Access Until: 2015-08-05
Appears in Collections:Cornell Theses and Dissertations

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