Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (5): 1459-1476.doi: 10.1007/s10473-020-0517-7

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INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL

Tao SU, Guobao ZHANG   

  1. Colloge of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
  • Received:2018-10-29 Revised:2020-02-24 Online:2020-10-25 Published:2020-11-04
  • Contact: Guobao ZHANG E-mail:zhanggb2011@nwnu.edu.cn
  • Supported by:
    This work was supported by NSF of China (11861056), Gansu Provincial Natural Science Foundation (18JR3RA093).

Abstract: This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder's fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant $c^{*}$ such that when $c>c^{*}$, the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with $c=c^{*}$ is also established by a limiting argument and a delicate analysis of the boundary conditions. Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed $c

Key words: predator-prey system, ratio-dependent functional response, discrete diffusion, invasion traveling waves

CLC Number: 

  • 34A33
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