Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics. This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure. By constructing a proper Poincar ′e map of the non-smooth system, an analytical expression of the Jacobian matrix of Poincar′e map is given. Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge–Kutta method. When the period is fixed and the coupling strength changes, the system undergoes stable, periodic, quasi-periodic, and hyper-chaotic solutions, etc. The Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.