JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 85-94.doi: 10.6040/j.issn.1671-9352.0.2017.509

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Hopf bifurcation and spatial patterns in a delayed diffusive predator-prey system with Holling-III functional response and linear harvesting effect

ZHANG Dao-xiang, SUN Guang-xun, MA Yuan, CHEN Jin-qiong, ZHOU Wen   

  1. School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241002, Anhui, China
  • Received:2017-09-27 Online:2018-04-20 Published:2018-04-13

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Abstract: The spatial dynamics in a delayed diffusive predator-prey system with Holling-III functional response and linear harvesting effect is studied. Firstly, the local stability of positive equilibrium of the system and the condition of Hopf bifurcation are obtained by using the stability theory and the bifurcation theory. Secondly, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem.Furthermore, the instability of Hopf bifurcation leads to the formation of spatial pattern of system. Finally, the correctness of the theoretical results is verified by numerical simulations, which shows that the system has rich dynamic behavior.

Key words: predator-prey system, Hopf bifurcation, Holling-III functional response, delay

CLC Number: 

  • O175.21
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