Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T01:25:54.904Z Has data issue: false hasContentIssue false
  • English
  • Français

Homoclinic solutions for coupled systems of differential equations

Published online by Cambridge University Press:  14 November 2011

P. Grindrod  and
B. D. Sleeman
P. Grindrod
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4HN
B. D. Sleeman
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4HN
Get access Rights & Permissions [Opens in a new window]

Synopsis

Topological ideas based on the notion of flows and Wazewski sets are used to establish the existence of homoclinic orbits to a class of Hamiltonian systems. The results, as indicated, are applicable to a variety of reaction diffusion equations including models of bundles of unmyelinated nerve axons.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 319 - 328
Copyright
Copyright © Royal Society of Edinburgh 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Conley, C. C.. Isolated invariant sets and the Morse index (Conference Board of the Mathematical Sciences 38) (Providence, R.I.: AMS, 1978).CrossRefGoogle Scholar
2Dunbar, S. R.. Travelling wave solutions of diffusive Lotka-Volterra Equations. J. Math. Biol. 12 (1983), 11–32.Google Scholar
3Grindrod, P. and Sleeman, B. D.. Qualitative analysis of reaction diffusion systems modelling coupled unmyelinated nerve axons. J. Math. Appl. Med. Biol. (to appear).Google Scholar
4Smoller, J. A.. Shock wanes and reaction diffusion equations (New York: Springer, 1983).CrossRefGoogle Scholar
5Smoller, J. A. and Wasserman, A.. Global bifurcation of steady-state solutions. J. Differential Equations 39 (1981), 269–290.CrossRefGoogle Scholar
6Hofer, H. and Toland, J.. Homoclinic, heteroclinic and periodic orbits for a class of indefinite Hamiltonian systems. Preprint.Google Scholar
7Hartman, P.. Ordinary differential equations (Boston: Birkhäuser, 1982).Google Scholar