Fractional-order PD control at Hopf bifurcations in delayed fractional-order small-world networks
Autor: | Wei Xing Zheng, Min Xiao, Guo-Ping Jiang, Jinde Cao, Lindu Zhao, Jinxing Lin |
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Rok vydání: | 2017 |
Předmět: |
Hopf bifurcation
0209 industrial biotechnology Computer Networks and Communications Applied Mathematics Saddle-node bifurcation 02 engineering and technology Heteroclinic bifurcation Bifurcation diagram 01 natural sciences Biological applications of bifurcation theory symbols.namesake 020901 industrial engineering & automation Pitchfork bifurcation Bifurcation theory Transcritical bifurcation Control and Systems Engineering Control theory 0103 physical sciences Signal Processing symbols 010301 acoustics Mathematics |
Zdroj: | Journal of the Franklin Institute. 354:7643-7667 |
ISSN: | 0016-0032 |
Popis: | Bifurcation and control of fractional-order systems are still an outstanding problem. In this paper, a novel delayed fractional-order model of small-world networks is introduced and several topics related to the dynamics and control of such a network are investigated, such as the stability, Hopf bifurcations, and bifurcation control. The nonlinear interactive strength is chosen as the bifurcation parameter to analyze the impact of the interactive strength parameter on the dynamics of the fractional-order small-world network model. Firstly, the stability domain of the equilibrium is completely characterized with respect to network parameters, delays and orders, and some explicit conditions for the existence of Hopf bifurcations are established for the delayed fractional-order model. Then, a fractional-order Proportional-Derivative (PD) feedback controller is first put forward to successfully control the Hopf bifurcation which inherently happens due to the change of the interactive parameter. It is demonstrated that the onset of Hopf bifurcations can be delayed or advanced via the proposed fractional-order PD controller by setting proper control parameters. Meanwhile, the conditions of the stability and Hopf bifurcations are obtained for the controlled fractional-order small-world network model. Finally, illustrative examples are provided to justify the validity of the control strategy in controlling the Hopf bifurcation generated from the delayed fractional-order small-world network model. |
Databáze: | OpenAIRE |
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