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.
Effects of seasonal growth on ratio dependent delayed prey predator system
✍ Scribed by Sunita Gakkhar; Kuldeep Negi; Saroj Kumar Sahani
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 992 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1007-5704
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✦ Synopsis
The Beddington-DeAngelis ratio dependent prey predator model with time delay has been discussed. The existence of Hopf bifurcation has been established. The numerical simulations have shown that seasonal growth and delay can give rise to variety of attractors including periodic, quasi-periodic as well as chaotic oscillations. The degree of complexity in the system increases with increase in magnitude of delay, or frequency of seasonal variation. The model parameters involved in functional response can also affect the complexity of the system.
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