Oscillation deduced from the Neimark-Sacker bifurcation in a discrete dual Internet congestion control algorithm

Advances in Difference Equations

Yingguo Li¹ 

[1]School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, P.R. China

关键词: dual congestion control;    Neimark-Sacker bifurcation;    stability;    time delay;    discrete dynamic system;   

DOI  :  10.1186/1687-1847-2013-136

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider a dual Internet congestion control algorithm applied to a nonstandard finite-difference scheme, which responds to congestion signals from the network. By choosing delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcations are analyzed. Then the explicit algorithm for determining the direction of Neimark-Sacker bifurcations and the stability of invariant closed curves are derived. In addition, we give specific examples to illustrate the phenomenon that coincides with our theoretical results. MSC:34K18, 34K20.

【 授权许可】

CC BY