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Guckenheimer's research in this area is aimed at "extending the qualitative theory of dynamical systems to apply to systems with multiple time scales". Examples of systems with multiple time scales include neural systems and switching controllers.
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Guckenheimer's research has also included the development of computer methods used in studies of nonlinear systems. He has overseen the development of DsTool, an interactive software laboratory for the investigation of dynamical systems.
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of periodic orbits as well as "generate rigorous computer proofs of the qualitative properties of numerically computed dynamical systems".
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329:(with A. R. Willms, D. J. Baro and R. M. Harris-Warrick), J. Comp. Neuroscience 6 (1999), 145–168.
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Computing periodic orbits and their bifurcations with automatic differentiation
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341:(with K. Hoffman and W. Weckesser), SIAM J. App. Dyn. Sys. 2 (2002), 1–35.
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Nonlinear
Oscillations, Dynamical Systems and Bifurcation of Vector Fields
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Nonlinear
Oscillations, Dynamical Systems and Bifurcation of Vector Fields
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directly. His research in this area attempts to automatically compute
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The forced van der Pol equation I: the slow flow and its bifurcations
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Guckenheimer studies dynamical models of a small neural system, the
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He became a SIAM Fellow in 2009. In 2012 he became a fellow of the
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Presidents of the
Society for Industrial and Applied Mathematics
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An improved parameter estimation method for
Hodgkin-Huxley model
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335:(with B. Meloon), SIAM J. Sci. Stat. Comp. 22 (2000), 951–985.
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Dr. John
Guckenheimer's research has focused on three areas —
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Fellows of the
Society for Industrial and Applied Mathematics
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323:, Journal of Experimental Mathematics 4 (1995), 153–164.
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Phase portraits of planar vector fields: computer proofs
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Fellows of the
American Academy of Arts and Sciences
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List of
Fellows of the American Mathematical Society
317:(with Philip Holmes), Springer-Verlag, 1983, 453 pp.
156:(born 1945) joined the Department of Mathematics at
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518:"John M. Guckenheimer, Professor of Mathematics"
235:of crustaceans — attempting to learn more about
255:, Guckenheimer has constructed a new family of
243:is modified by chemical and electrical inputs.
239:, the ways in which the rhythmic output of the
305:), and he gave the Moser Lecture in May 2015.
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549:Theoretical & Applied Mechanics home page
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271:Dynamics in systems with Multiple Time Scales
623:Fellows of the American Mathematical Society
469:http://fellows.siam.org/index.php?sort=last
168:in 1984, and was elected president of the
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593:University of California, Berkeley alumni
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301:in 2013 for his book (coauthored with
603:21st-century American mathematicians
598:20th-century American mathematicians
500:. Cornell University. Archived from
446:. Cornell University. Archived from
375:. Cornell University. Archived from
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162:University of California, Santa Cruz
126:University of California, Santa Cruz
544:Department of Mathematics home page
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633:People from Baton Rouge, Louisiana
203:) is an extensively cited work on
160:in 1985. He was previously at the
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233:stomatogastric ganglion
164:(1973-1985). He was a
154:John Mark Guckenheimer
23:John Mark Guckenheimer
16:American mathematician
559:Dr. John Guckenheimer
309:Selected publications
299:Leroy P. Steele Prize
98:Leroy P. Steele Prize
520:. Cornell University
516:John Guckenheimer.
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418:Cornell University
184:, where his Ph.D.
158:Cornell University
130:Cornell University
88:Bifurcation theory
68:Harvard University
397:John Guckenheimer
289:Awards and honors
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45:Baton Rouge
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508:2008-03-31
490:References
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428:2008-03-31
414:"Research"
383:2008-03-31
257:algorithms
251:Employing
195:His book
49:Louisiana
444:"DsTool"
211:Research
182:Berkeley
176:and his
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399:at the
174:Harvard
280:DsTool
199:(with
112:Fields
100:(2013)
94:Awards
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178:Ph.D.
75:(PhD)
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241:STG
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