Journal Article

The periodic competing Lotka–Volterra model with impulsive effect

Bing Liu and Lansun Chen

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 2, pages 129-145
Published in print June 2004 | ISSN: 1477-8599
Published online June 2004 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/21.2.129
The periodic competing Lotka–Volterra model with impulsive effect

More Like This

Show all results sharing these subjects:

  • Applied Mathematics
  • Biomathematics and Statistics

GO

Show Summary Details

Preview

In this paper, the dynamic behaviour of a classical periodic Lotka–Volterra competing system with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equations, some conditions are obtained for the linear stability of the trivial and semi‐trivial periodic solutions. It is proved that the system can be permanent if all the trivial and semi‐trivial periodic solutions are linearly unstable. We use standard bifurcation theory to show the existence of nontrivial periodic solutions which arise near the semi‐trivial periodic solution. As an application, a fish harvest problem is considered. We explain how two competing species, one of which in a periodic environment without impulsive effect would be doomed to extinction, can coexist with suitably periodic impulsive harvesting.

Keywords: competing system; impulsive effect; extinction; coexistence; bifurcation

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.