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Volume 4 Issue 2
Apr.  2017

IEEE/CAA Journal of Automatica Sinica

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Min Xiao, Guoping Jiang, Jinde Cao and Weixing Zheng, "Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 361-369, Apr. 2017. doi: 10.1109/JAS.2016.7510151
Citation: Min Xiao, Guoping Jiang, Jinde Cao and Weixing Zheng, "Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 361-369, Apr. 2017. doi: 10.1109/JAS.2016.7510151

Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms

doi: 10.1109/JAS.2016.7510151
Funds:

This work was supported by National Natural Science Foundation of China 61573194

This work was supported by National Natural Science Foundation of China 61374180

This work was supported by National Natural Science Foundation of China 61573096

China Postdoctoral Science Foundation Funded Project 2013M530229

China Postdoctoral Science Special Foundation Funded Project 2014T70463

Six Talent Peaks High Level Project of Jiangsu Province ZNDW-004

Science Foundation of Nanjing University of Posts and Telecommunications NY213095

and Australian Research Council DP120104986

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  • In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay, the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.

     

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