Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays
We consider a predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by anal...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/930762 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We consider a predator-prey system with Beddington-DeAngelis functional
response and delays, in which not only the stage structure on prey but also the
delay due to digestion is considered. First, we give a sufficient and necessary condition
for the existence of a unique positive equilibrium by analyzing the corresponding
locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov
function, we prove that the positive equilibrium is locally asymptotically stable
under a sufficient condition. Finally, by using comparison theorem and the ω-limit set
theory, we study the global asymptotic stability of the boundary equilibrium and the
positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the
global asymptotic stability. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |