Dynamic optimal control at Hopf bifurcation of a Newman–Watts model of small-world networks via a new PD1n scheme

Lingzhi Si, Min Xiao, Zhengxin Wang, Chengdai Huang, Zunsgui Cheng, Binbin Tao and Fengyu Xu

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: In this paper, a neoteric fractional-order Proportional–Derivative (PD) feedback controller is proposed to address the problem of bifurcation control for an integer-order small-world network model with discrete delay. The time delay is selected as the bifurcation parameter, and sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed by analyzing the stability of the controlled system. By regulating the controller parameters, the dynamic behavior for the controlled system can be effectively optimized. Finally, by simulating numerical examples, theoretical derivations are verified and the relationships between the onset of the Hopf bifurcation and the controller parameters are obtained.

Keywords: Bifurcation control; Fractional-order PD controller; Small-world network; Time delays (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310337

DOI: 10.1016/j.physa.2019.121769

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