非线性脉冲状态依赖捕食-被捕食模型的定性分析

王刚; 唐三一

doi:10.3879/j.issn.1000-0887.2013.05.008

非线性脉冲状态依赖捕食-被捕食模型的定性分析

doi: 10.3879/j.issn.1000-0887.2013.05.008

王刚,
唐三一

陕西师范大学数学与信息科学学院, 西安 710062

基金项目: 国家自然科学基金资助项目(11171199)

详细信息

作者简介:
王刚(1985—), 男, 湖北人，硕士(E-mail: wanggang19851213@126.com)；唐三一(1970—), 男, 教授, 博士(通讯作者. E-mail:sytang@snnu.edn.cn).

中图分类号: O241.8; O242
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出版历程
- 收稿日期: 2013-04-03
- 修回日期: 2013-05-03
- 刊出日期: 2013-05-15

Qualitative Analysis of Prey-Predator Model With Nonlinear-Impulsive Effects

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062,P.R.China

摘要

摘要: 由于资源的有限性以及害虫群体对杀虫剂的抗性发展等因素,使得杀虫剂对害虫的杀死率具有饱和效应．因此,当害虫的数量达到经济阈值时, 杀虫剂对害虫的杀死率与经济阈值有关．为了刻画上述饱和效应,建立了一类非线性脉冲状态依赖捕食被捕食模型．利用Lambert W函数和脉冲半动力系统的相关技巧,分析了模型阶1正周期解的存在性和稳定性, 得到了相应的充分条件．进而讨论了非线性脉冲与线性脉冲对阶1周期解存在性的影响.
- 非线性脉冲 /
- 捕食被捕食系统 /
- 阶1周期解 /
- 存在性 /
- 稳定性
Abstract: Due to the limited resources as well as the development of pests’ resistance to pesticides, the instant killing rate of pesticide applications with respect to the pest could depend on the density of pest populations. Thus, the instant killing rate is a function of economic threshold ET once the density of pest population reaches the ET and integrated control tactics are implemented. In order to depict the saturation effects, a prey-predator model with nonlinear state-dependent impulsive effects was proposed. Using the Lambert W function and the analytical techniques of the impulsive semi-dynamical system, the sufficient conditions which guaranteed the existence, local and global stability of order 1 positive periodic solution of the proposed model were obtained. Further, the effects of nonlinear impulse on the existence of order 1 periodic solution was discussed.
- nonlinear pulse /
- preypredator model /
- order 1 periodic solution /
- existence /
- stability

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参考文献(10)

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