Stability Switch Boundaries in an Internet Congestion Control Model with Diverse Time delays
Stability Switch Boundaries in an Internet Congestion Control Model with Diverse Time delays
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DOI：
10.1142/s0218127413300164
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发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
Shu Zhang;K. Chung;Jian Xu
中科院分区：
文献类型：
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作者：
Shu Zhang;K. Chung;Jian Xu
针对具有不同时延的二维拥塞控制模型，详细研究了稳定切换边界在时延平面上的几何性质。根据系统参数，得到了稳定切换边界为垂直类螺线、水平类螺线、对角类螺线和闭环系统的条件。边界曲线可以自相交或彼此相交。其中一些交叉点被认为是余维为3的切线双Hopf分叉。结果表明，无论其他系统参数取值如何，在时滞平面内都存在双Hopf分岔点。
For a two-dimensional congestion control model with diverse time delays, this paper provides a detailed study on the geometrical properties of stability switch boundaries in the plane of time delays. Conditions for stability switch boundaries to arise as vertical spiral-like curves, horizontal spiral-like curves, diagonal spiral-like curves and closed-loops are obtained on the system parameters other than time delays. The boundary curves may self-intersect or intersect with one another. Some of these intersections are identified as tangent double Hopf bifurcation with codimension three. It is found that double Hopf bifurcation point exists in the plane of time delays regardless of the values of the other system parameters.