Global bifurcations of a multi-stable nonlinear oscillator

In this paper, we focus on the bifurcation analysis of a multi-stable nonlinear oscillator. This oscillator exhibits multiple equilibrium configurations depending on the parameter of a mechanical model. It is shown that the equilibrium curve undergoes multiple fold bifurcations, a supercritical pitchfork bifurcation, multiple discontinuous bifurcations, and multiple hysteresis bifurcations. Additionally, multiple solutions and different forms of bifurcation are observed for certain parameter values. Moreover, different response orbits under different initial conditions are emphasized by adopting the generalized cell mapping method.