Construction of the Fitzhugh-Nagumo Pulse Using Differential Forms
- C. JonesAffiliated withDepartment of Mathematics, University of Maryland
- , N. KopellAffiliated withDepartment of Mathematics, Boston University
- , R. LangerAffiliated withSky Computers, Inc.
Systems of singularly perturbed ordinary differential equations can often be solved approximately by singular solutions. These singular solutions are pieced together from solutions to simpler sets of equations obtained as limits from the original equations. There is a large body of literature on the question of when the existence of a singular solution implies the existence of an actual solution to the original equations. Techniques that have been used include fixed point arguments (Conley , Carpenter , Hastings  and Gardner and Smoller ), implicit function theorem and related functional-analytic techniques (Fife , Fujii et al. , Hale and Sakamoto [7,8]) differential inequalities (see for instance Chang and Howes ) and nonstandard analysis (Diener and Reeb ).
- Construction of the Fitzhugh-Nagumo Pulse Using Differential Forms
- Book Title
- Patterns and Dynamics in Reactive Media
- pp 101-115
- Print ISBN
- Online ISBN
- Series Title
- The IMA Volumes in Mathematics and its Applications
- Series Volume
- Series ISSN
- Springer New York
- Copyright Holder
- Springer-Verlag New York Inc.
- Additional Links
- eBook Packages
- Editor Affiliations
- 2. Department of Chemical Engineering and Material Science, University of Minnesota
- 3. School of Mathematics, University of Minnesota
- 4. Physics Department and the Center for Nonlinear Dynamics, University of Texas
- Author Affiliations
- 5. Department of Mathematics, University of Maryland, USA
- 6. Department of Mathematics, Boston University, USA
- 7. Sky Computers, Inc., USA
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