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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (9): 83-90.doi: 10.6040/j.issn.1671-9352.0.2021.500

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一类Beddington-DeAngelis-Tanner型扩散捕食系统的稳定性和Turing不稳定性

孙春杰,张存华*   

  1. 兰州交通大学数理学院, 甘肃 兰州 730070
  • 发布日期:2022-09-15
  • 作者简介:孙春杰(1995— ),女,硕士研究生,研究方向为非线性动力学. E-mail:chunjiesun2021@163.com*通信作者简介:张存华(1972— ),女,副教授,研究方向为非线性动力学. E-mail:chzhang71@163.com
  • 基金资助:
    国家自然科学基金资助项目(61563026)

Stability and Turing instability in the diffusive Beddington-DeAngelis-Tanner predator-prey model

SUN Chun-jie, ZHANG Cun-hua*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2022-09-15

摘要: 考虑带有齐次Neumann边界条件的Beddington-DeAngelis-Tanner型扩散捕食系统。通过分析系统在唯一正常数平衡解处线性化系统的特征值问题,获得该系统正常数平衡解的局部渐近稳定性和Turing不稳定性。用MATLAB软件包对所获得的理论结果进行适当的数值模拟。

关键词: 扩散捕食系统, 局部渐近稳定性, Turing不稳定性

Abstract: The diffusive Beddington-DeAngelis-Tanner predator-prey model with Neumann boundary condition is considered. By using the linearization method and analyzing the distribution of the eigenvalues of the associated eigenvalue problem on the complex plane, the local asymptotic stability and Turing instability of the unique constant positive equilibrium solution are obtained. The numerical simulation using MATLAB software package is carried out to verify the theoretical results obtained.

Key words: diffusive predator-prey model, local asymptotic stability, Turing instability

中图分类号: 

  • O175.26
[1] XU Xiaofeng, LIU Ming. Global Hopf bifurcation of a general predator-prey system with diffusion and stage structures[J]. Journal of Differential Equations, 2020, 269(10):8370-8386.
[2] TANG Xiaosong, SONG Yongli. Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator-prey model with herd behavior[J]. Appl Math Comput, 2015, 254:375-391.
[3] MANNA D, MAITI A, SAMANTA G P. Analysis of a predator-prey model for exploited fish populations with schooling behavior[J]. Appl Math Comput, 2018, 317:35-48.
[4] JIANG Heping. Turing bifurcation in a diffusive predator-prey model with schooling behavior[J]. Appl Math Lette, 2019, 96:230-235.
[5] XIA Lei, SUN Jiaojiao, YIN Zuguang, et al. Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances[J]. Applied Mathematics and Mechanics, 2021, 42(8):1123-1134.
[6] QIU Shuyuan, MU Chunlai, TU Xinyu. Dynamics for a three-species predator-prey model with density-dependent motilities[J]. Journal of Dynamics and Differential Equations, 2021, 33:1-25.
[7] MAY R M. Stability and complexity in model ecosystems[M]. New Jersey: Princeton University Press, 1973: 89-96.
[8] TANNER J T. The stability and intrinsic growth rates of prey and predator populations[J]. Ecology, 1975, 56:855-867.
[9] YAN Xiangping, ZHANG Cunhua. Stability and turing instability in a diffusive predator-prey system with Beddington-DeAngelis function response[J]. Nonlinear Analysis: Real World Applications, 2014, 20(20):1-13.
[10] ARANCIBIA I C, BODE M, FLORES J, et al. Turing patterns in a diffusive Holling-Tanner predator-prey model with an alternative food source for the predator[J]. Communications in Nonlinear Science and Numerical Simulation, 2021, 99:1-15.
[11] 程惠东, 侯晓雨.具有Holling-Tanner功能反应的捕食模型研究[J].数学建模及其应用, 2021,10(2):32-43. CHENG Huidong, HOU Xiaoyu. Study on the predator-prey model with Holling-Tanner functional response[J]. Mathematical Modeling and Its Applications, 2021, 10(2):32-43.
[1] 周艳,张存华. 具有集群行为的捕食者-食饵反应扩散系统的稳定性和Turing不稳定性[J]. 《山东大学学报(理学版)》, 2021, 56(7): 73-81.
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