数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 537-548.doi: 10.1016/S0252-9602(16)30019-4

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POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY

杨璐1, 张贻民2   

  1. 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
    2. Key Laboratory of Applied Mathematics and Complex Systems, Gansu 730000, China;
    3. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • 收稿日期:2014-11-11 修回日期:2015-10-12 出版日期:2016-04-25 发布日期:2016-04-25
  • 通讯作者: Yimin ZHANG,E-mail:zhangyimin@wipm.ac.cn E-mail:zhangyimin@wipm.ac.cn
  • 基金资助:

    The research was supported by the National Natural Science Foundation of China (11361053, 11201204, 11471148, 11471330, 145RJZA112).

POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY

Lu YANG1, Yimin ZHANG2   

  1. 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China;
    2. Key Laboratory of Applied Mathematics and Complex Systems, Gansu 730000, China;
    3. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Received:2014-11-11 Revised:2015-10-12 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    The research was supported by the National Natural Science Foundation of China (11361053, 11201204, 11471148, 11471330, 145RJZA112).

摘要:

In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.

关键词: Predator-prey system, steady state solution, dynamical behavior

Abstract:

In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.

Key words: Predator-prey system, steady state solution, dynamical behavior

中图分类号: 

  • 35J20