一类具有非线性脉冲的捕食与被捕食系统的定性分析

李畅通

doi:10.21656/1000-0887.400226

一类具有非线性脉冲的捕食与被捕食系统的定性分析

doi: 10.21656/1000-0887.400226

李畅通^1,2

¹西安工业大学理学院, 西安 710021;²陕西师范大学数学与信息科学学院, 西安 710062

基金项目: 国家自然科学基金(61772017）

详细信息

作者简介:
李畅通(1982—), 男, 博士生(E-mail: lctnihao@snnu.edu.cn).

中图分类号: Q241.8|O242
计量
- 文章访问数: 1533
- HTML全文浏览量: 309
- PDF下载量: 308
- 被引次数: 0
出版历程
- 收稿日期: 2019-07-23
- 修回日期: 2019-08-29
- 刊出日期: 2020-05-01

Analysis of the Predator-Prey Model With Nonlinear Impulsive Control

LI Changtong^1,2

¹School of Science, Xi’an Technological University, Xi’an 710021, P.R.China;²School of Mathematics and Information Science, Shaanxi Normal University,Xi’an 710062, P.R.China

Funds: The National Natural Science Foundation of China(61772017）

摘要

摘要: 实际的害虫控制策略由于受到资源有限、种群密度的影响,具有饱和效应或非线性特征.因此,该文对一类具有非线性脉冲控制策略的捕食与被捕食模型进行了全局定性分析.利用脉冲微分方程中的Floquet 理论和比较方法,得到模型的天敌根除周期解全局渐近稳定的充分条件,通过分支理论，得到非平凡周期解存在性的条件,数值模拟验证了具有非线性脉冲的模型具有非常复杂的动态行为.
- 全局稳定 /
- 周期解 /
- 非线性脉冲 /
- 害虫控制
Abstract: Due to limited resources and population densities, the actual pest control strategies such as spraying pesticide and releasing natural enemies have saturation effects or nonlinearity. Therefore, a predator-prey model with nonlinear impulsive control due to resource limitation was proposed and analyzed. With the Floquet theory and the differential comparison principle, the condition for global stability of the predator-free periodic solution was provided. It is shown that once a threshold condition is met, a stable nontrivial periodic solution will emerge via a supercritical bifurcation. The numerical results show that the predator-prey model with nonlinear pulse has rich dynamical behaviors.
- globally stable /
- periodic solution /
- nonlinear pulse /
- pest control

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参考文献(16)

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