Singular limits for travelling waves for a pair of equations

Royal Society of Edinburgh - Proceedings A

Volumn 126, Issue 2, 1996, Pages 399-411

  Hutson, Vivian ^a   Mischaikow, Konstantin ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344456926     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500022812     Document Type: Article

References (16)

1. J. Alexander, R. Gardner and C. Jones. A topological invariant arising in the stability analysis of travelling waves. J. Reine Angew. Math. 410 (1990), 167-212.
2. C. Conley. Isolated Invariant Sets and the Morse Index, CBMS Lecture Notes 38 (Providence, RI: American Mathematical Society, 1978).
3. C. Conley and P. Fife. Critical manifolds, travelling waves, and an example from population genetics. J. Math. Biol. 14 (1982), 159-76.
4. C. Conley and R. Gardner. An application of the generalized Morse index to travelling wave solutions of a competitive reaction diffusion model. Indiana Univ. Math. J. 33 (1989), 319-43.
5. 4. Trans. Amer. Math. Soc. 286 (1984), 557-96.
6. P. C. Fife. Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics 28 (New York: Springer, 1979).
7. R. Gardner. Existence of travelling wave solution of predator-prey systems via the Conley index. SIAM J. Math. Anal. 13 (1982), 167-79.
8. R. Gardner and C. Jones. Stability of traveling wave solutions of diffusive predator-prey systems. Trans. Amer. Math. Soc. 327 (1991), 465-524.
9. V. Hutson. Stability in a reaction diffusion model of mutualism. SIAM J. Math. Anal. 17 (1986), 58-66.
10. V. Hutson, R. Law and D. Lewis. Dynamics of ecologically obligate mutualisms - effects of spatial diffusion on resilience of the interacting species. American Naturalist 126 (1985), 465-9.
11. C. Jones, T. Kapitula and J. Powell. Nearly real fronts in a Ginzburg-Landau equation. Proc. Roy. Soc. Edinburgh Sect. A 116 (1990), 193-206.
12. J. Keener. Frequency dependent decoupling of parallel excitable fibers. SIAM J. Appl. Math. 49 (1989), 210-30.
13. K. Mischaikow and V. Hutson. Travelling waves for mutualist species. SIAM J. Math. Anal. 24 (1993), 987-1008.
14. K. Mischaikow and J. Reineck. Travelling waves in predator-prey systems. SIAM J. Math. Anal. 24 (1993), 1179-214.
15. Y. Nishiura, M. Mimura, H. Ikeda and H. Fujii. Singular limit analysis of stability of traveling wave solutions in bistable reaction-diffusion systems. SIAM J. Math. Anal. 21 (1990), 85-122.
16. D. Salamon. Connected simple systems and the Conley index of isolated invariant sets. Trans. Amer. Math. Soc. 291 (1985), 1-41.