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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (2): 219-242.doi: 10.3969/j.issn.1005-3085.2019.02.008

• • 上一篇    

具有阶段结构的脉冲三种群捕食--食饵系统的动力学性质研究（英）

刘   钦,   邵远夫,   周   斯,   陈海茹   

  1. 桂林理工大学理学院，桂林  541004
  • 收稿日期:2017-06-12 接受日期:2018-03-20 出版日期:2019-04-15 发布日期:2019-06-15
  • 通讯作者: 邵远夫 E-mail address: shaoyuanfu@163.com
  • 基金资助:
    国家自然科学基金(11161015;11861027)；广西自然科学基金(2016GXNSFAA380194).

Dynamical Behaviors of a Three Species Predator-prey System with Predator Stage-structure and Impulsive Effects

LIU Qin,  SHAO Yuan-fu,  ZHOU Si,  CHEN Hai-ru   

  1. School of Science, Guilin University of Technology, Guilin 541004
  • Received:2017-06-12 Accepted:2018-03-20 Online:2019-04-15 Published:2019-06-15
  • Contact: Y. Shao. E-mail address: shaoyuanfu@163.com
  • Supported by:
    The National Natural Science Foundation of China (11161015; 11861027); the Natural Science Foundation of Guangxi (2016GXNSFAA380194).

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摘要： 考虑不同时刻的脉冲效应和捕食者的阶段结构因素的影响，本文构建了一个具有阶段结构的脉冲三种群捕食--食饵模型．利用Floquent定理和小振幅扰动等方法，证明了食饵灭绝周期解存在性、稳定性和全局吸引性．运用比较定理并构建适当的Laypunov函数，证明了系统持久性．最后，通过数值仿真得到了物种的时间序列图和系统的混沌图，并验证了理论结果的准确性．

关键词: 阶段结构, 脉冲, 持久性, 数值模拟

Abstract: Considering the impulsive effects at different fixed moments and the predator stage-structure, we propose a three species predator-prey system with predator stage-structure and impulsive effects in this paper. At first, we prove the existence, stability and global attractivity of the prey-extinction periodic solution via the Floquent theory and small amplitude perturbation. Then, we obtain the permanence of this system by using comparison method and involving multiple Laypunov functions. Finally, we show our theoretical results by numerical simulations, such as time series of species population and chaotic bands of system.

Key words: stage-structure, impulsive, permanence, numerical simulation

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