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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (4): 439-450.doi: 10.3969/j.issn.1005-3085.2019.04.007

• • 上一篇    下一篇

一类带有恐惧效应的捕食-食饵模型的定性分析

王  蓉1,  杨文彬2,  李艳玲1   

  1. 1- 陕西师范大学数学与信息科学学院，西安  710062
    2- 西安邮电大学理学院，西安  710121
  • 收稿日期:2017-05-27 接受日期:2018-01-08 出版日期:2019-08-15 发布日期:2019-10-15
  • 通讯作者: 李艳玲 E-mail: yanlingl@snnu.edu.cn
  • 基金资助:
    国家自然科学基金(61672021)；陕西省教育厅专项科研计划项目(16JK1710).

Qualitative Analysis of a Class of Predator-prey Model with Fear Effect

WANG Rong1,  YANG Wen-bin2,  LI Yan-ling1   

  1. 1- School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
    2- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121
  • Received:2017-05-27 Accepted:2018-01-08 Online:2019-08-15 Published:2019-10-15
  • Contact: Y. Li. E-mail address: yanlingl@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61672021); the Special Scientific Research Project of Education Department of Shaanxi Province (16JK1710).

PDF (PC)

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摘要： 反应扩散系统解的性质蕴含了丰富的信息，对于刻画种群生态现象有着重要的意义．本文研究了一类带有恐惧效应的捕食-食饵模型平衡态正解问题．首先，利用最值原理，得到平衡态正解的先验估计，为后续问题的研究奠定了基础；其次，给出了正常数平衡解的唯一存在的充分条件，并借助线性稳定性理论，得到了正常数平衡解的稳定性；最后，根据度理论，得到非常数正解的存在性．

关键词: 捕食-食饵模型, 恐惧效应, 稳定性, 平衡态解, 度理论

Abstract: The nature of the reaction-diffusion system solution contains abundant information, which is of great significance to the study of population ecological phenomena. In this paper, the existence of positive solutions to the steady-state system of a predator-prey model with fear effect is studied. Firstly, some priori estimates of positive constant steady-state solution are obtained using the maximum principle, which lay the foundation for the subsequent research. Secondly, the sufficient condition of the unique existence for the equilibrium solution is given, and the stability of positive constant steady-state solution is discussed using the stability theory of linear operators. Finally, on the basis of the degree theory, the existence of non-constant steady-state solution is given.

Key words: predator-prey model, fear effect, stability, steady-state solution, degree theory

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