Amplitude control of limit cycle in a van der Pol Duffing system |
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Authors: | Ouyang Ke-Jian Tang Jia-Shi Liang Cui-Xiang |
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Affiliation: | College of Civil Engineering, Hunan University, Changsha 410082, China; College of Mechanics and Aerospace, Hunan University, Changsha 410082, China |
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Abstract: | This paper applies washout filter technology to amplitudecontrol of limit cycles emerging from Hopf bifurcation of the van derPol--Duffing system. The controlling parameters for the appearanceof Hopf bifurcation are given by the Routh--Hurwitz criteria.Noticeably, numerical simulation indicates that the controllerscontrol the amplitude of limit cycles not only of the weakly nonlinear vander Pol--Duffing system but also of the strongly nonlinear van derPol--Duffing system. In particular, the emergence of Hopf bifurcationcan be controlled by a suitable choice of controlling parameters.Gain-amplitude curves of controlled systems are also drawn. |
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Keywords: | bifurcation control limit cycle Hopf bifurcation vander Pol--Duffing system |
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