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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Moirogiannis, Dimitrios"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Marcelo O. Magnasco"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-01-01T08:00:00Z","date_published":"2019-01-01T08:00:00Z","updated_at":"2026-07-24T04:11:45Z","subjects":["nonhyperbolic dynamics","center manifold","neural systems","dynamical systems theory","invariant subspace","neural computation","Life Sciences"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/502","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Marcelo O. Magnasco"]},{"key":"dc:creator","label":"Author","values":["Moirogiannis, Dimitrios"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonhyperbolic dynamics","center manifold","neural systems","dynamical systems theory","invariant subspace","neural computation","Life Sciences"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/502"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Center Manifold Dynamics in Randomly Coupled Oscillators and in Cochlea"]}]}],"canonical_facts":{"dc:contributor":["Marcelo O. Magnasco"],"dc:creator":["Moirogiannis, Dimitrios"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/502"],"dc:subject":["nonhyperbolic dynamics","center manifold","neural systems","dynamical systems theory","invariant subspace","neural computation","Life Sciences"],"dc:title":["Center Manifold Dynamics in Randomly Coupled Oscillators and in Cochlea"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:11:45Z"}