Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 62, Issue 9, Pages 4819-4826Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2688583
Keywords
Congestion control; fractional-order dynamical systems; hopf bifurcation; stability
Funding
- National Natural Science Foundation of China [61573194, 61374180, 61573096]
- Six Talent Peaks High Level Project of Jiangsu Province of China [2014-ZNDW-004]
- Science Foundation of Nanjing University of Posts and Telecommunications [NY213095]
- Australian Research Council [DP120104986]
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In this technical note, fractional-order congestion control systems are introduced for the first time. In comparison with the conventional integer-order dual congestion control algorithms, the fractional control algorithms are more accurate and versatile. Bifurcation theory in fractional-order differential equations is still an outstanding problem. Sufficient conditions for the occurrence of Hopf bifurcations are extended from integer-order dynamical systems to fractional-order cases. Then, these conditions are used to establish the existence of Hopf bifurcations for the delayed fractional-order model of dual congestion control algorithms proposed in this note. Finally, the onsets of bifurcations are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Illustrative examples are also provided to demonstrate the theoretical results.
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