Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.11.11
  • Accepted : 2017.09.05
  • Published : 2018.01.01
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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.

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References

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