Mathematical Sciences: Topics in Theory and Application of  Hopf Bifurcation
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
This is a computational project aimed at developing                         scientific software for analysis of Hopf bifurcation. Work in                   three distinct areas within Hopf bifurcation theory is proposed.                1. Location and analysis of Hopf bifurcations in delay                          differential equations, and the general eigenvalue problem for                  these equations.  2. Numerical algorithms for continuation of                   periodic solutions of delay differential systems.  3. Unfolding                 of Hopf bifurcations for ordinary differential equations.                           The first project includes new methods for testing linear                   stability of systems of delay differential equations and will                   build on the existing software for the ordinary differential                    equations. Adaptation of this software to the case of delay                     differential equations presents a number of difficulties, one of                them being the numerical computation of eigenvalues.                                The second project aims at developing computational methods                 for finding families of periodic solutions corresponding to                     various values of the parameter in the equation. Methods such as                piecewise polynomial approximation with collocation at Gauss-                   Legendre points and a variant of LU decomposition will be used to               solve the problem.                                                                  The third project involves calculating higher order expansion               terms of a germ fuction by possibly combining symbolic and                      numerical computing.                                                                All three projects have some analytic components and                        applications to specific equations arising in various other areas               of research.  One of the models included in the investigation is                the Hodgkin-Huxley current-clamped nerve conduction model.                      These projects are intended to yield computer codes of wider                    applicability than the specific systems studied.                                    This research falls into the general area of computational                  methods for mathematical analysis of problems described by                      ordinary and functional differential equations. Such equations                  are often used to describe dynamical phenomena in physics,                      engineering and biology.
{'FirstName': 'Brian', 'LastName': 'Hassard', 'PI_MID_INIT': 'D', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Brian D Hassard', 'EmailAddress': None, 'NSF_ID': '000169558', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'SUNY at Albany', 'CityName': 'Albany', 'ZipCode': '122220100', 'PhoneNumber': '5184374974', 'StreetAddress': '1400 Washington Ave MSC 312', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '20', 'CONGRESS_DISTRICT_ORG': 'NY20', 'ORG_DUNS_NUM': '152652822', 'ORG_LGL_BUS_NAME': 'RESEARCH FOUNDATION FOR THE STATE UNIVERSITY OF NEW YORK, THE', 'ORG_PRNT_DUNS_NUM': '020657151'}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
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