Crises and chaotic transients of a tristable magnetoelastic oscillator

In this paper, we focus on the global dynamical analysis of a tristable magnetoelastic nonlinear oscillator. The bifurcation diagrams of the excitation amplitude and the excitation frequency are determined by numerical integration, and the largest Lyapunov exponents are carried out by using Wolf's method. Global properties of the systems are emphasized by adopting the generalized cell mapping method. Attractors, saddles, basins of attraction, basin boundaries, and invariant manifolds are plotted. As the excitation amplitude and the excitation frequency increase, the chaotic transients are recorded, and the boundary crises are observed. Furthermore, the validity and rationality of the results from the generalized cell mapping method are verified via directly numerical integration.