Homogenization and propagation in the bistable equation

Physica D: Nonlinear Phenomena

Volumn 136, Issue 1-2, 2000, Pages 1-17

  Keener, J P ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Bistable equation; Homogenization; Propagation failure; Resistive inhomogeneity

Indexed keywords

EID: 0346057259     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00151-7     Document Type: Article

References (17)

1. D.G. Aronson, H.F. Weinberger, Nonlinear diffusion in population genetics, combustion and nerve propagation, in: Lecture Notes in Mathematics, vol. 446, Springer, London, 1975, pp. 5-49.
2. A.R. Champneys, Homoclinic orbits in reversible systems and their application in mechanics, fluids, and optics, Physica D 112 (1998) 158-186.
3. S.N. Chow, J.K. Hale, J. Mallet-Paret, An example of bifurcation to homoclinic orbits, J. Differential Equations 37 (1980) 351-373.
4. J.D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, MA, 1968.
5. C.E. Elmer, E.S. Van Vleck. Analysis and computation of traveling waves solutions of bistable differential-difference equations, Nonlinearity 12 (1999) 771-798.
6. G. Fath, Propagation failure of traveling waves in a discrete bistable medium, Physica D 116 (1998) 176-190.
7. P. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, vol. 28, Springer, Berlin, 1979.
8. P.C. Fife, J.B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Rat. Mech. Anal. 65 (1977) 335-361.
9. J.K. Hale, Ordinary Differential Equations, Pure and Applied Mathematics, vol. XXI, Wiley-Interscience, New York, 1969.
10. P. Holmes, J. Marsden, J. Scheurle, Exponentially small splittings of separatrices with applications to KAM theory and degenerate bifurcations, Cont. Math. 81 (1988) 213-243.
11. J.P. Keener, Chaotic behavior in slowly varying systems of nonlinear differential equations, Stud. Appl. Math. 67 (1982) 25-44.
12. J.P. Keener, Propagation and its failure in coupled systems of discrete excitable cells, SIAM J. Appl. Math. 47 (1987) 556-572.
13. J.P. Keener, Principles of Applied Mathematics: Transformation and Approximation, Addison-Wesley, Reading, MA, 1988.
14. J.P. Keener, The effects of discrete gap junction coupling on propagation in myocardium, J. Theor. Biol. 148 (1991) 49-82.
15. J.P. Keener, Direct activation and defibrillation of cardiac tissue, J. Theor. Biol. 178 (1996) 313-324.
16. J.P. Keener, Propagation of waves in an excitable medium excitable with discrete release sites, SIAM J. Appl. Math., to appear.
17. B. Zinner, Existence of traveling wavefront solutions for the discrete Nagumo equation, J. Differential Equations 96 (1992) 1-27.