Nonlinear Vibrations by Periodic Perturbation in a Murali–Lakshmanan–Chua Electronic Circuit Combined with Multiple Frequency Signal

Abstract

In this paper, a detailed investigation of oscillation behaviors in the non-autonomous Murali–Lakshmanan–Chua (MLC) circuit is proposed. The determination of the bifurcation value in the MLC circuit is associated with the two switching boundaries leading to different types of nonlinearity in structures. The non-conventional bifurcations in the layer equations by switching manifolds are explored. The discontinuous Fold/Fold and Hopf/Hopf periodic vibration mechanisms can be well released. The influence of the addition of the second periodic force is also being discussed. We use Clarke’s concept of generalised differential to analyze the occurrence of discontinuous Hopf bifurcations. The DeMoivre expansion formula and the variable replacing method are used to express the relevant critical manifold. The validity for our study is also elucidated by numerical examples of application. Complex oscillation patterns under periodic perturbation with multiple-frequency signal as well as the underlying characteristic properties are demonstrated. The MLC circuit occurs the transitions through the sets of non-smooth bifurcation values leading to complicated wave forms. The addition of second periodic signal will provide the parameter condition to acquire more desired periodic vibrations.