ZHAO Yufeng.Dynamic analysis of a infected prey - predator stochastic model with saturation incidence[J].Journal of Yanbian University,2023,(04):298-307.
一类具有饱和发生率的染病食饵- 捕食者随机模型的动力学分析
- Title:
- Dynamic analysis of a infected prey - predator stochastic model with saturation incidence
- 文章编号:
- 1004-4353(2023)04-0298-10
- 关键词:
- 染病食饵- 捕食者随机模型; 饱和发生率; Holling Ⅲ型功能反应函数; 比率依赖; 平稳分布; 灭绝
- Keywords:
- infected prey - predator stochastic model; saturation incidence; Holling - type Ⅲ functional response function; ratio - dependent; stationary distribution; extinction
- 分类号:
- O175.12
- 文献标志码:
- A
- 摘要:
- 研究了一类带有饱和发生率和随机比率依赖的Holling Ⅲ型功能反应的染病食饵- 捕食者随机模型.首先,利用It?公式和构造的Lyapunov函数证明了染病食饵- 捕食者随机模型存在唯一的全局正解.其次,利用Has’miniskii遍历性理论证明了随机模型存在唯一的遍历平稳分布.再次,利用It?公式、大数定律、鞅理论得到了染病食饵种群的阈值Rh0: 当Rh0<1时疾病将趋于灭绝,当Rh0>1时疾病将长期存在.最后,利用数值仿真验证了所得结果的正确性.
- Abstract:
- In this paper, we investigated the dynamics of a stochastic ratio - dependent infected prey - predator model with saturation incidence and Holling - type Ⅲ functional response.Firstly, we proved that the unique solution of stochastic model was globally positive by using It? formula and constructing Lyapunov function.Secondly, the existence of a unique ergodic stationary distribution was studied by using the ergodicity theory of Has’miniskii.Thirdly, the threshold Rh0 for the infected prey population was obtained by using It? formula, the law of large numbers, and the martingale theory, that is, the disease will tend to extinction if Rh0<1, and it will exist for a long time if Rh0>1.Finally, numerical simulations were used to verify the correctness of the obtained results.
参考文献/References:
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备注/Memo
收稿日期: 2023-06-16
基金项目: 山西省高等学校科技创新计划项目(2022L645); 山西省高等学校教学改革创新项目(J20221313); 山西省教育科学“十四五”规划课题(GH-220495)
作者简介: 赵玉凤(1985—),女,硕士,讲师,研究方向为生物数学.