JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 53-61.doi: 10.6040/j.issn.1671-9352.0.2018.262

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Coexistence solution of a predator-prey system with B-D functional response and toxin effects

FENG Xiao-zhou1, XU Min2, WANG Guo-hui3   

  1. 1. College of Science, Xian Technological University, Xian 710021, Shaanxi, China;
    2. Shaanxi Aerospace Electromechanical Environment Engineering Design Institute Co., Ltd., Xian 710100, Shaanxi, China;
    3. College of Optoelectronic Engineering, Xian Technological University, Xian 710021, Shaanxi, China
  • Online:2018-12-20 Published:2018-12-18

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Abstract: The steady state of a predator-prey system with B-D reaction term and toxin effect under the homogeneous Dirichlet boundary condition is investigated. First, using the principle of maximum value and the comparison principle of eigenvalues, we give some prior estimates of coexistence solution on the system and obtain the necessary condition of non-coexistence solution. Secondly, by using the Leray-Schauder degree theory, the calculation of the fixed point index, the maximum principle and the method of upper and lower solutions, the sufficient condition for the existence of the coexistence solution is established. Finally, the local asymptotic stability of the trivial solution and the semi-trivial solution of the steady state system is proved by using the linearization operator and the Riesz-Schauder theory.

Key words: B-D functional response, predator-prey system, coexistence, stability

CLC Number: 

  • O175.26
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