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一类具时滞和阶段结构的捕食模型的稳定性与Hopf分支
  • ISSN号：1000-4424
  • 期刊名称：《高校应用数学学报：A辑》
  • 时间：0
  • 分类：O175.1[理学—数学;理学—基础数学]
  • 作者机构：[1]军械工程学院应用数学研究所,河北石家庄050003
  • 相关基金：国家自然科学基金（10671209）
作者： 田晓红[1], 徐瑞[1]
关键词： 捕食系统, 时滞, 功能性反应, HOPF分支, 稳定性, predator-prey system, time delay, functional response, Hopf bifurcation, stability
中文摘要：

研究一类具有时滞和阶段结构的捕食模型的稳定性和Hopf分支的存在性问题．通过分析特征方程，得到了正平衡点局部稳定的条件．同时，应用中心流形定理和规范型理论，得到了确定Hopf分支方向和分支周期解的稳定性的计算公式．最后对所得理论结果进行了数值模拟．

英文摘要：

A stage-structured predator-prey model with time delay and Holling type Ⅲ functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulas are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.

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期刊信息
  • 《高校应用数学学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:浙江大学 中国工业与应用数学学会
  • 主编：林正炎 李大潜
  • 地址：杭州市玉泉浙江大学数学系
  • 邮编：310027
  • 邮箱：amjcu@zjy.edu.cn
  • 电话：0571-87951602
  • 国际标准刊号：ISSN：1000-4424
  • 国内统一刊号：ISSN：33-1110/O
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,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:3669