Investigating bifurcation points of an impact oscillator

Investigating the dynamical properties of mechanical systems has been an attractive topic recently. In this paper, the dynamical properties of an impact oscillator are studied. The impact oscillator is a non-autonomous system with possible chaotic attractors. The oscillator without external force has a stable equilibrium. Bifurcation analysis of the system shows various dynamics by changing the frequency ratio of external force. In addition, plotting bifurcation diagrams with different methods indicates the system’s multistability. The bifurcation points of the system are studied. Prediction of bifurcation points is critical since it can cause unwanted qualitative changes in the dynamic of the system. Autocorrelation and Lyapunov exponent are used in the prediction of the bifurcation points of this system.