Analysis of stability and Hopf bifurcation for a delayed logistic equation
- 作者：Chengjun Sun ; Maoan Han and Yiping Lin
- 刊名：Chaos ; Solitons and Fractals
- 出版年：2007
- 期刊代码：5_09600779
- 类别：ph
- 出版时间：February 2007
- 卷：31
- 期：3
- 页码：672-682
- 文件大小：224 K
摘要
The dynamics of a logistic equation with discrete delay are investigated, together with the local and global stability of the equilibria. In particular, the conditions under which a sequence of Hopf bifurcations occur at the positive equilibrium are obtained. Explicit algorithm for determining the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation are derived by using the theory of normal form and center manifold [Hassard B, Kazarino D, Wan Y. Theory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981.]. Global existence of periodic solutions is also established by using a global Hopf bifurcation result of Wu [Symmetric functional differential equations and neural networks with memory. Trans Amer Math Soc 350:1998;4799–38.]