Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (4): 9-22,31.doi: 10.3969/j.issn.1000-5641.2018.04.002

Previous Articles     Next Articles

Spatial Turing pattern of a predator-prey system with nonlinear harvesting effect

ZHANG Dao-xiang1, SUN Guang-xun1, HU Wei1, KAI Ge2   

  1. 1. School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241002, China;
    2. College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China
  • Received:2017-09-20 Online:2018-07-25 Published:2018-07-19

Abstract: We study the formation and selection of Turing patterns for a class of predator-prey systems with nonlinear harvesting effect. Firstly, the conditions of Turing instability induced by cross-diffusion terms are given by stability theory, and the existence region of Turing patterns of the system are obtained by bifurcation theory. Secondly, the amplitude equations of the system are derived using the multi-scales analysis method, and the selection results of Turing patterns are given. Finally, Matlab is used to simulate the pattern formation and selection results of the system. The results show that the system has rich Turing patterns, such as spot, stripe, and coexistence of the two types.

Key words: predator-prey system, Hopf bifurcation, Turing patterns, amplitude equation

CLC Number: