Student Theses and Dissertations

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


In dynamical systems theory, a fixed point of the activity is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees the local existence of an invariant subspace of the activity, known as a center manifold, around nonhyperbolic fixed points. A growing number of theoretical and experimental studies suggest that neural systems utilize dynamics on center manifolds to display complex, nonlinear behavior and to flexibly adapt to wide-ranging sensory input parameters. In this thesis, I will present two lines of research exploring nonhyperbolicity in neural dynamics.


A Thesis Presented to the Faculty of The Rockefeller University in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy

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