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J4 ›› 2012, Vol. 47 ›› Issue (11): 109-118.

• 数学 • 上一篇    下一篇

具有干扰和分段常数变量模型的稳定性及分支

陈斯养,刘晓娜   

  1. 陕西师范大学数学与信息科学学院,陕西 西安 710062
  • 收稿日期:2011-12-26 出版日期:2012-11-20 发布日期:2012-11-26
  • 作者简介:陈斯养 (1955- ), 男, 副教授, 硕士研究生导师, 研究方向为生态数学与数学建模.Email:chsy398@126.com
  • 基金资助:

    国家自然科学基金资助项目(10871122; 11171119)

Stability and bifurcation analysis of the model with interference and piecewise constant variables

CHEN Si-yang, LIU Xiao-na   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2011-12-26 Online:2012-11-20 Published:2012-11-26

摘要:

讨论了一类具有干扰和分段常数变量的单种群模型稳定性及分支问题。基于特征值理论,得到了正平衡点局部渐近稳定的充要条件,利用中心流形定理和分支理论分析了Flip分支和Hopf分支的存在条件。最后应用Matlab软件进行数值模拟,并验证了所得定理的正确性。

关键词: 干扰; 稳定性; Flip分支;Hopf分支

Abstract:

 The stability and bifurcation of a single-species with interference and piecewise constant variables were discussed. Based on the theory of characteristic value, the necessary and sufficient conditions of the local asymptotically stability were obtained. The existence of Flip bifurcation and Hopf bifurcation were investigated by using center manifold argument and bifurcation theory. Some numerical simulations were performed by Matlab to verify the theoretical results.

Key words: interference; stability; Flip bifurcation; Hopf bifurcation

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