Abstract
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.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
