Amplitude control of limit cycle in a van der Pol Duffing system

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.