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非线性脉冲状态依赖捕食被捕食模型的定性分析
  • ISSN号：1000-0887
  • 期刊名称：应用数学和力学
  • 时间：2013.5.15
  • 页码：496-505
  • 分类：O241.8[理学—计算数学;理学—数学] O242[理学—计算数学;理学—数学]
  • 作者机构：[1]陕西师范大学数学与信息科学学院,西安710062
  • 相关基金：国家自然科学基金资助项目（11171199）
  • 相关项目：综合害虫治理与Bt作物抗性管理的数学模型研究
作者： 王刚|唐三一|
关键词： 非线性脉冲, 捕食被捕食系统, 阶1周期解, 存在性, 稳定性, nonlinear pulse, prey-predator model, order 1 periodic solution, existence, stabil-ity
中文摘要：

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LambertW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．

英文摘要：

Due to the limited resources as well as the development of pests＇ resistance to pesti-cides, 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 thresh-old （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 analyti-cal techniques of the impulsive semi-dynanucal system, the sufficient conditions which guaran-teed the existence, local and global stability of order 1 positive periodic solution of the pro-posed model were obtained. Further, the effects of nonlinear impulse on the existence of order 1 periodic solution was discussed.

同期刊论文项目
综合害虫治理与Bt作物抗性管理的数学模型研究
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期刊信息
  • 《应用数学和力学》
  • 中国科技核心期刊
  • 主管单位:重庆交通大学
  • 主办单位:重庆交通大学
  • 主编：钟万勰
  • 地址：重庆南岸区重庆交通大学90信箱
  • 邮编：400074
  • 邮箱：applmathmech@cqjtu.edu.cn
  • 电话：023-62652450
  • 国际标准刊号：ISSN：1000-0887
  • 国内统一刊号：ISSN：50-1060/O3
  • 邮发代号:78-21
  • 获奖情况:
  • 国际工程索引（EI）收录期刊,我国力学类核心期刊,中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,日本日本科学技术振兴机构数据库,美国应用力学评论,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:8965