Mathematical Sciences: Dynamical Systems and Neural Networks
{'Code': '07010000', 'Directorate': {'Abbreviation': 'ENG', 'LongName': 'Directorate For Engineering'}, 'Division': {'Abbreviation': 'ECCS', 'LongName': 'Div Of Electrical, Commun & Cyber Sys'}}
{'SignBlockName': 'Paul Werbos', 'PO_EMAI': None, 'PO_PHON': None}
This project combines related work in dynamical systems and neural              networks.  The P.I. will investigate the dynamics of certain types              of difference schemes and closely related systems of nonlinear                  differential equations.  These systems depend on parameters that                fluctuate either deterministically or stochastically.  These                    results will be used to evaluate the convergence of the weigh                   dynamics in several kinds of supervised learning schemes for                    adaptive neural networks, including Widrow-Hoff associative                     learning and Barto-Anandan reinforcement learning.  The P.I. will               also investigate a neural network model of retinal development in               fluctuating environments due to Amari and Takeuchi.                                                                                                             In competitive and cooperative systems of differential equations,               the P.I. will extend earlier work to obtain convergence theorems                applicable to the activation dynamics of certain types of                       recurrent neural networks having asymmetrical fixed weights.  A                 separate study will try to prove that dissipative competitive                   systems in R3, and a restricted class of such systems in R4, can                be approximated by structurally stable ones, and satisfy a C'                   Closing lemma for all r&gt;2.  This would establish new classes of                 structurally stable systems, and would be the first proof of a                  nontrivial C2 closing lemma in dimensions &gt;3.
{'FirstName': 'Morris', 'LastName': 'Hirsch', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Morris W Hirsch', 'EmailAddress': 'hirsch@math.berkeley.edu', 'NSF_ID': '000450832', 'StartDate': '08/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Berkeley', 'CityName': 'BERKELEY', 'ZipCode': '947101749', 'PhoneNumber': '5106433891', 'StreetAddress': '1608 4TH ST STE 201', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'CA12', 'ORG_UEI_NUM': 'GS3YEVSS12N6', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF CALIFORNIA, THE', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '1494', 'Text': 'NEUROENGINEERING'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8807813.xml'}