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

This paper applies washout filter technology to amplitude control of limit cycles emerging from Hopf bifurcation of the van der Pol–Duffing system. The controlling parameters for the appearance of Hopf bifurcation are given by the Routh–Hurwitz criteria. Noticeably, numerical simulation indicates that the controllers control the amplitude of limit cycles not only of the weakly nonlinear van der Pol–Duffing system but also of the strongly nonlinear van der Pol–Duffing system. In particular, the emergence of Hopf bifurcation can be controlled by a suitable choice of controlling parameters. Gain-amplitude curves of controlled systems are also drawn.