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http://dx.doi.org/10.4134/JKMS.j160717

BIFURCATION OF A PREDATOR-PREY SYSTEM WITH GENERATION DELAY AND HABITAT COMPLEXITY  

Ma, Zhihui (School of Mathematics and Statistics Lanzhou University)
Tang, Haopeng (School of Mathematics and Statistics Lanzhou University)
Wang, Shufan (School of Mathematics and Computer Science Northwest University for Nationalities)
Wang, Tingting (School of Mathematics and Statistics Lanzhou University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 43-58 More about this Journal
Abstract
In this paper, we study a delayed predator-prey system with Holling type IV functional response incorporating the effect of habitat complexity. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. The explicit formulas which determine the direction and stability of Hopf bifurcation are obtained by the normal form theory and the center manifold theorem.
Keywords
predator-prey system; time delay; Holling IV type functional response; Habitat complexity; Hopf bifurcation;
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