Global dynamics for a nonsmooth dynamical system induced by wing rock

The aim of this paper is to investigate global dynamics for a nonsmooth dynamical system, which is a mathematical model of the wing rock [18]. Since the system is only Lipschitz continuous and not $ C^1 $, many classical results cannot be applied to the system. We also demonstrate that the system possesses abundant nonlinear dynamics, such as generalized Hopf bifurcation, generalized pitchfork bifurcation, heteroclinic bifurcation and double limit cycle bifurcation. Then, we present the global bifurcation diagram and global phase portraits in the Poincaré disc.