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- Title
The existence of positive solutions for a predator-prey model with Ivlev functional response.
- Authors
Ma Xiao-li
- Abstract
The steady-state problem of the predator-prey model with Ivlev functional response is studied. The existence of positive solutions is established. By means of fixed point index of compact maps in cones, combining with maximum principles and lower-upper solution methods, sufficient conditions for coexistence are obtained. The results show that if the birth rate of predator is smaller than the critical value which is required to survive in the absence of prey, two species can co-existed as long as the birth rate of prey is larger than the critical value. On the other hand, if the birth rate of predator is larger than the critical value which is required to survive in the absence of prey, and the birth rate of prey is not too small, two species can also co-existed.
- Subjects
SOCIAL indicators; INTERNATIONAL relations; LOTKA-Volterra equations; CONES (Operator theory); ANIMAL specialists
- Publication
Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao, 2011, Vol 24, Issue 2, p212
- ISSN
1006-8341
- Publication type
Article