JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (09): 88-94.doi: 10.6040/j.issn.1671-9352.0.2014.582

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Coexistence solutions for a predator-prey model with additive Allee effect and a protection zone

LI Hai-xia   

  1. School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
  • Received:2014-12-26 Revised:2015-03-06 Online:2015-09-20 Published:2015-09-26

Abstract: A diffusive predator-prey model with additive Allee effect and a protection zone is discussed. Firstly, the stability of trivial and semi-trivial solutions is investigated. Secondly, the non-existence of non-constant positive solutions is determined. Finally, the existence of non-constant positive solutions is obtained by using the global bifurcation theory. Under weakly Allee effect, the results indicate that the two species will coexist and the coexistence solutions are stable when the diffusion coefficient is suitably chosen and the parameters satisfy certain conditions. Furthermore, the two species cannot coexist when the diffusion coefficients are sufficiently large.

Key words: protection zone, bifurcation theory, additive Allee effect

CLC Number: 

  • O175.26
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