## 留言板

 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
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.

• 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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