Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm |
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Authors: | Dawei Ding Jie Zhu Xiaoshu Luo Yuliang Liu |
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Affiliation: | 1. Key Lab. of Intelligent Computing & Signal Processing, Anhui University, Hefei 230039, China;2. Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;3. Department of Physics and Electronic Science, Guangxi Normal University, Guilin 541004, China |
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Abstract: | This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing communication delay as the bifurcation parameter, we demonstrate that the system loses its stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Moreover, the bifurcating periodic solution of the system is calculated by means of the perturbation method. Discussion of stability of the periodic solutions involves the computation of Floquet exponents by considering the corresponding Poincaré–Lindstedt series expansion. Finally, numerical simulations for verifying the theoretical analysis are provided. |
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