Skip Navigation

IMA Journal of Mathematical Control and Information 2000 17(4):395-413; doi:10.1093/imamci/17.4.395
© 2000 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by PETTET, G. J.
Right arrow Articles by NORBURY, J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Lotka-Volterra equations with chemotaxis: walls, barriers and travelling waves

G. J. PETTET, D. L. S. MCELWAIN and J. NORBURY

Centre in Statistical Science and Industrial Mathematics, School of Mathematical Sciences, Queensland University of Technology GPO Box 2434, Brisbane 4001, Australia
Mathematical Institute, University of Oxford 24–29 St Giles', Oxford OX1 3LB, UK

In this paper we consider a simple two species model for the growth of new blood vessels. The model is based upon the Lotka-Volterra system of predator and prey interaction, where we identify newly developed capillary tips as the predator species and a chemoattractant which directs their motion as the prey. We extend the Lotka-Volterra system to include a one-dimensional spatial dependence, by allowing the predators to migrate in a manner modelled on the phenomenon of chemotaxis. A feature of this model is its potential to support travelling wave solutions. We emphasize that in order to determine the existence of such travelling waves it is essential that the global relationships of a number of phase plane features other than the equilibria be investigated.

Keywords: chemotaxis; travelling waves; Lotka-Volterra; angiogenesis; wound healing; phase plane analysis.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.