Torus T2 and its locking, doubling, chaos of a vibro-impact system

► The nonlinear dynamics of a 3-d.o.f vibro-impact system is modeled. ► The double Neimark-Sacker bifurcation and generation of the torus T2 are analyzed. ► The changes into multi-circle torus T1, periodic orbit and routes to chaos of the torus T2 are investigated.