一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析

doi:10.13371/j.cnki.chin.q.j.m.2023.01.001

数学季刊 ›› 2023, Vol. 38 ›› Issue (1): 1-19.doi: 10.13371/j.cnki.chin.q.j.m.2023.01.001

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一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析

School of Mathematics and Information Science, Zhengzhou University of Light Industry,
Zhengzhou 450002, China

收稿日期:2022-07-08 出版日期:2023-03-30 发布日期:2023-03-20
通讯作者: LI Yong-feng (1980-), female, native of Shangqiu, Henan, professor of Zhengzhou University of Light Industry, engages in differential equations and dynamic systems E-mail: yfli2003@163.com
作者简介: LI Yong-feng (1980-), female, native of Shangqiu, Henan, professor of Zhengzhou University of Light Industry, engages in differential equations and dynamic systems; ZHU Cheng-zhi (1996-), male, native of Yuxi, Yunnan, postgraduate of Zhengzhou University of Light Industry, engages in differential equations and dynamic systems; LIU Yan-wei (1978-), male, native of Zhoukou, Henan, lecturer of Zhengzhou University of Light Industry, engages in applied mathematics.
基金资助:
Supported by the National Natural Science Foundation of China (Grant No. 11901541);
The Scientific and Technological Key Projects of Henan Province (Grant No. 202102310631); The Key Scientific
Research Project in Colleges and Universities of Henan Province of China (Grant No. 19A110036).

Dynamic Analysis of a Predator-Prey Model with State-Dependent Impulsive Effects

School of Mathematics and Information Science, Zhengzhou University of Light Industry,
Zhengzhou 450002, China

Received:2022-07-08 Online:2023-03-30 Published:2023-03-20
Contact: LI Yong-feng (1980-), female, native of Shangqiu, Henan, professor of Zhengzhou University of Light Industry, engages in differential equations and dynamic systems E-mail: yfli2003@163.com
About author: LI Yong-feng (1980-), female, native of Shangqiu, Henan, professor of Zhengzhou University of Light Industry, engages in differential equations and dynamic systems; ZHU Cheng-zhi (1996-), male, native of Yuxi, Yunnan, postgraduate of Zhengzhou University of Light Industry, engages in differential equations and dynamic systems; LIU Yan-wei (1978-), male, native of Zhoukou, Henan, lecturer of Zhengzhou University of Light Industry, engages in applied mathematics.
Supported by:
Supported by the National Natural Science Foundation of China (Grant No. 11901541);
The Scientific and Technological Key Projects of Henan Province (Grant No. 202102310631); The Key Scientific
Research Project in Colleges and Universities of Henan Province of China (Grant No. 19A110036).

摘要/Abstract

摘要： In this paper, a pest-dependent model and integrated pest management
strategy is proposed, that is, when pest populations reach levels that impair economic
development, we will use a combination of strategies, such as biological, cultural and
chemical control strategies reduce pests to a reasonable level. First, we investigated the
system without control measures, and discussed the existence and stability of equilibria,
we also proved the system has no limit cycle. Then, a state feedback impulsive model is
constructed, the existence and uniqueness of the order-one periodic solution are proved
by means of the successor function method to confirm the feasibility of the biological and
chemical control strategy of pest management. Secondly, the stability of system is proved
by the analogue of the Poincar ´ e criterion. Finally, we give an example and numerical
simulations to explain the mathematical conclusions.

关键词: Predator-prey model, State feedback, Period solution, Stability

Abstract: In this paper, a pest-dependent model and integrated pest management
strategy is proposed, that is, when pest populations reach levels that impair economic
development, we will use a combination of strategies, such as biological, cultural and
chemical control strategies reduce pests to a reasonable level. First, we investigated the
system without control measures, and discussed the existence and stability of equilibria,
we also proved the system has no limit cycle. Then, a state feedback impulsive model is
constructed, the existence and uniqueness of the order-one periodic solution are proved
by means of the successor function method to confirm the feasibility of the biological and
chemical control strategy of pest management. Secondly, the stability of system is proved
by the analogue of the Poincar ´ e criterion. Finally, we give an example and numerical
simulations to explain the mathematical conclusions.

Key words: Predator-prey model, State feedback, Period solution, Stability

中图分类号:

O187.1

李永凤, 朱城志, 刘艳伟. 一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析[J]. 数学季刊, 2023, 38(1): 1-19.

LI Yong-feng, ZHU Cheng-zhi, LIU Yan-wei. Dynamic Analysis of a Predator-Prey Model with State-Dependent Impulsive Effects[J]. Chinese Quarterly Journal of Mathematics, 2023, 38(1): 1-19.

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一类具有状态依赖脉冲影响的捕食者-食饵模型动力学分析

Dynamic Analysis of a Predator-Prey Model with State-Dependent Impulsive Effects

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