Hopf bifurcation in a fractional diffusion food-limited models with feedback control

被引：0
作者：
Wenzhen Gan
Canrong Tian
Peng Zhu
机构：
[1] Jiangsu university of Technology,School of Mathematics and Physics
[2] Yancheng Institute of Technology,Department of Basic Sciences
来源：
Journal of Mathematical Chemistry | 2015年 / 53卷
关键词：
Fractional diffusion; Time delay; Hopf bifurcation; Spiral pattern;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the direction and stability of Hopf bifurcation induced by time delay in a food-limited models with feedback control and fractional diffusion. By means of analyzing eigenvalue spectrum, we show that the positive equilibrium is locally asymptotically stable in the absence of time delay, but loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold. Using the norm form and the center manifold theory, we investigate the stability and direction of the Hopf bifurcation. The stability of the Hopf bifurcation leads to the emergence of spatial spiral patterns. Numerical calculations are performed to illustrate our theoretical results.
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页码：1393 / 1411
页数：18
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