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Bifurcation control of small‐world networks with delays VIA PID controller
Author(s) -
Tao Binbin,
Xiao Min,
Jiang Guoping,
Sun Qingshan
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1958
Subject(s) - pid controller , control theory (sociology) , mathematics , hopf bifurcation , controller (irrigation) , bifurcation , saddle node bifurcation , center manifold , period doubling bifurcation , stability (learning theory) , biological applications of bifurcation theory , bifurcation theory , control (management) , computer science , control engineering , nonlinear system , engineering , physics , temperature control , agronomy , artificial intelligence , quantum mechanics , machine learning , biology
In this paper, the problem of bifurcation control for a small‐world network model with time delay is studied. We first put forward a Proportional‐Integral‐Derivative (PID) feedback scheme to control the Hopf bifurcation of the network. The time delay is selected as the bifurcation parameter. The conditions of the stability and Hopf bifurcation are given for the controlled network. By using the center manifold theorem and the normal form theory, the direction and stability of bifurcating periodic solutions are confirmed. The feasible region of the parameters of the controller is determined. It is found that the bifurcation dynamics of the small‐world network are optimized by adjusting the parameters of the PID controller. Finally, a numerical example verifies the effectiveness of the designed PID controller, and the relationships between the onset of the Hopf bifurcation and the control parameters are obtained.