JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 76-84.doi: 10.6040/j.issn.1671-9352.0.2017.580

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Global bifurcation structure in a predator-prey model with a spatial degeneracy

DONG Ya-ying   

  1. School of Science, Xian Polytechnic University, Xian 710048, Shaanxi, China
  • Received:2017-11-14 Online:2018-04-20 Published:2018-04-13

Abstract: A predator-prey model with Holling type II response function in a spatially degenerate heterogeneous environment is studied. When the prey growth rate is weak, a priori estimates of any positive steady-state solution is first obtained by the comparison principle, and then we show that the set of positive steady-state solutions forms a bounded global bifurcation curve by the global bifurcation theory. When the prey growth rate is strong, a priori estimates of any positive steady-state solution is first obtained by using reduction to absurdity, and then we show that the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory.

Key words: Holling II, global bifurcation, a priori estimates, spatial degeneracy

CLC Number: 

  • O175.26
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