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具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为

陈乾君 蒋媛 刘子建 谭远顺

陈乾君,蒋媛,刘子建,谭远顺. 具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为 [J]. 应用数学和力学,2022,43(4):453-468 doi: 10.21656/1000-0887.420203
引用本文: 陈乾君,蒋媛,刘子建,谭远顺. 具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为 [J]. 应用数学和力学,2022,43(4):453-468 doi: 10.21656/1000-0887.420203
CHEN Qianjun, JIANG Yuan, LIU Zijian, TAN Yuanshun. Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth[J]. Applied Mathematics and Mechanics, 2022, 43(4): 453-468. doi: 10.21656/1000-0887.420203
Citation: CHEN Qianjun, JIANG Yuan, LIU Zijian, TAN Yuanshun. Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth[J]. Applied Mathematics and Mechanics, 2022, 43(4): 453-468. doi: 10.21656/1000-0887.420203

具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为

doi: 10.21656/1000-0887.420203
基金项目: 国家自然科学基金(11801047);重庆市自然科学基金(cstc2019jcyj-msxm2151);重庆市教委基金(KJQN201900707);重庆市研究生导师团队建设项目(JDDSTD201802);重庆市高校创新研究群体项目(CXQT21021)
详细信息
    作者简介:

    陈乾君(1991—),女,硕士生(E-mail:1143451443@qq.com)

    刘子建(1982—),男,博士,硕士生导师(通讯作者. E-mail:hbliuzijian@126.com)

  • 中图分类号: O29

Dynamic Behavior of a Stochastic Predator Prey Model With the Gilpin-Ayala Growth

  • 摘要:

    该文研究了一类具有Gilpin-Ayala增长的随机捕食-食饵模型的动力学行为,证明了系统全局正解的存在性和唯一性,得到了灭绝性和持久性的充分条件。在此基础上,给出了控制捕食-食饵系统随机持久和灭绝的阈值,并且讨论了系统解的一些渐近性态。最后通过数值模拟,验证了结果的有效性。

  • 图  1  不考虑切换,例1参数下,两个子系统解的轨迹:(a) 子系统1,ξ(t)=1;(b) 子系统2,ξ(t)=2

    Figure  1.  The trajectories of the solutions to the 2 subsystems of example 1 without switching: (a) subsystem 1, ξ(t)=1; (b) subsystem 2, ξ(t)=2

    图  2  考虑切换,例1参数下,系统Markov链平稳分布时解的轨迹:(a) π=(0.7,0.3);(b) π=(1/3,2/3)

    Figure  2.  The trajectories of solutions in stationary distribution of system the Markov chain for example 1 with switching: (a) π=(0.7, 0.3); (b) π=(1/3, 2/3)

    图  3  不考虑切换,例2参数下,两个子系统解的轨迹:(a) 子系统1,ξ(t)=1,(σ(1),σ(2))=$ (\sqrt{0.12},\sqrt{0.82}) $;(b) 子系统2,ξ(t)=2,(σ(1),σ(2))=$ (\sqrt{0.82},\sqrt{0.12}) $

    Figure  3.  The trajectories of solutions to the 2 subsystems of example 2 without switching: (a) subsystem 1, ξ(t)=1, (σ(1), σ(2))=$ (\sqrt{0.12},\sqrt{0.82}) $; (b) subsystem 2, ξ(t)=2, (σ(1), σ(2))=$ (\sqrt{0.82},\sqrt{0.12}) $

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出版历程
  • 收稿日期:  2021-07-16
  • 修回日期:  2022-03-05
  • 网络出版日期:  2022-03-19
  • 刊出日期:  2022-04-01

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