A topological invariant arising in the stability analysis of travelling waves

Journal fur die Reine und Angewandte Mathematik

Volumn 1990, Issue 410, 1990, Pages 167-212

  Alexander, J ^a   Gardner, R ^b   Jones, C ^a  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005235678     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1990.410.167     Document Type: Article

References (30)

1. M. F. Atiyah, K-theory, New York 1967.
2. P. W. Bates and C. K. R. T. Jones, Invariant manifolds for semilinear partial differential equations, Dynamics Reported 2 (1988).
3. R. Bellman, Introduction to Matrix Analysis, New York 1960.
4. R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, New York 1964.
5. G. Carpenter, A geometric approach to singular perturbation problems with applications to nerve impulse equations, J. Diff. Equ. 23 (1977), 335-367.
6. W. A. Coppel, Dichotomies in Stability Theory, Lect. Notes in Math. 629, Berlin 1978.
7. J. W. Evans, Nerve axon equations, I: Linear approximations, Indiana Univ. Math. J. 21 (1972), 877-955.
8. J. W. Evans, Nerve axon equations, II: Stability at rest, Indiana Univ. Math. J. 22 (1972), 75-90.
9. J. W. Evans, Nerve axon equations, III: Stability of the nerve impulse, Indiana Univ. Math. J. 22 (1972), 577—594.
10. J. W. Evans, Nerve axon equations, IV: The stable and unstable impulse, Indiana Univ. Math. J. 24 (1975), 1169—1190.
11. N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971), 193—226.
12. P. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977), 335—361.
13. R. A. Gardner and C. K. R. T. Jones, Stability of travelling wave solutions of diffusive predator-prey systems, Trans. AMS, to appear.
14. P. Griffiths and J. Harris, Principles of Algebraic Geometry, New York 1971.
15. S. P. Hastings, On the existence of homoclinic and periodic orbits for the FitzHugh-Nagumo equations, Quart. J. Math. Oxford Ser. (2) 27 (1976), 123-134.
16. D. Henry, The geometric theory of semilinear parabolic equations, Lect. Notes in Math. 840, Berlin 1981.
17. D. Husemoller, Fibre Bundles, New York 1966.
18. H. Ikeda and M. Mimura, Personal communication.
19. C. K. R. T. Jones, Stability of the travelling wave solution of the FitzHugh-Nagumo system, Trans. AMS 286, No. 2 (1984), 431—469.
20. T. Kato, Perturbation Theory for Linear Operators, New York 1976.
21. N. J. Kopell, Weaves, shocks and target patterns in an oscillating chemical regent, in Nonlinear Diffusion, London 1977.
22. R. Langer, Existence of homoclinic travelling wave solutions to the FitzHugh-Nagumo equations, Ph. D. thesis, Northeastern University 1980.
23. K. Maginu, A geometrical condition for the instability of solitary travelling wave solutions in reaction-diffusion equations, preprint.
24. J. W. Milnor and J. D. Stasheff Characteristic Classes, Ann. of Math. Stud. 76, Princeton, NJ, 1974.
25. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Berlin 1983.
26. W. Rudin, Real and Complex Analysis, New York 1970.
27. D. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. in Math. 22 (1976), 312-355.
28. N. Steenrod, The Topology of Fibre Bundles, Princeton, NJ, 1951.
29. A. E. Taylor and D. Lay, Introduction to Functional Analysis, New York 1980.
30. E. Yanagida, Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol. 22 (1985), 81-104.