JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (11): 115-122.doi: 10.6040/j.issn.1671-9352.0.2016.282

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The stability of a predator-prey diffusion model with Beddington-DeAngelis functional response

FU Juan, ZHANG Rui, WANG Cai-jun, ZHANG Jing   

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Received:2016-06-17 Online:2016-11-20 Published:2016-11-22

Abstract: We consider a diffusive predator-prey model with Beddington-DeAngelis functional response. First, the local and global asymptotic stabilities of the nonnegative equilibrium point of weakly coupled reaction-diffusion system are obtained by linearization and constructing Lyapunov function. Secondly, the effect of cross-diffusion coefficient on the stability of the nonnegative equilibrium point is discussed. The results show that cross-diffusion can induce Turing unstable region.

Key words: self-diffusion, stability, cross-diffusion, lyapunov function, predator-prey model

CLC Number: 

  • O175.29
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