With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system in a periodic environment.
Convergence Results in a Well-Known Delayed Predator-Prey System
✍ Scribed by Edoardo Beretta; Yang Kuang
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 165 KB
- Volume
- 204
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
In this paper, we provide a detailed and explicit procedure of obtaining some Ž . regions of attraction for the positive steady state assumed to exist of a well known Lotka᎐Volterra type predator-prey system with a single discrete delay. Our procedure requires the delay length to be small. A detailed example is presented. The method used here is to construct a proper Liapunov functional in a restricted region.
📜 SIMILAR VOLUMES
A delayed Gause-type predator᎐prey system without dominating instantaneous negative feedbacks is investigated. It is proved that the system is uniformly persistent under some appropriate conditions. By means of constructing a suitable Lyapunov functional, sufficient conditions are derived for the lo