Premium
Bifurcation Control Of A Fractional‐Order Van Der Pol Oscillator Based On The State Feedback
Author(s) -
Xiao Min,
Jiang Guoping,
Zheng Wei Xing,
Yan Senlin,
Wan Youhong,
Fan Chunxia
Publication year - 2015
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.995
Subject(s) - van der pol oscillator , hopf bifurcation , control theory (sociology) , mathematics , bifurcation , saddle node bifurcation , period doubling bifurcation , controller (irrigation) , biological applications of bifurcation theory , bifurcation theory , nonlinear system , stability (learning theory) , transcritical bifurcation , physics , control (management) , computer science , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
In this paper, a dynamic state feedback is applied to control Hopf bifurcations arising from a fractional‐order Van Der Pol oscillator. The degree parameter indicating the strength of the nonlinear damping is chosen as the bifurcation parameter. It is shown that in the absences of the dynamic state feedback controller, the fractional‐order Van Der Pol oscillator loses the stability via the Hopf bifurcation early, and can maintain the stability only in a certain domain of the degree parameter. When applying the state feedback controller to the fractional‐order Van Der Pol oscillator, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the system possesses the stability in a larger parameter range. Numerical simulations are given to justify the validity of the dynamic state feedback controller in bifurcation controls.