Abstract:Both symmetric and asymmetric systems of one-degree-of-freedom double-impact Duffing oscillators are considered. The symmetry of Poincaré mapping is analyzed. By means of discontinuous mapping and the shooting method, periodic solution and its stability of the system are analyzed. Numerical simulation indicates that for the symmetric system, firstly a symmetric periodic orbit bifurcates into two antisymmetric period orbits, being of same stability, and the two antisymmetric periodic orbits go through two synchronous period-doubling bifurcations to form two antisymmetric chaotic attractors subsequently. Finally, the two antisymmetric chaotic attractors are fused into one symmetric chaotic attractor. For the asymmetric system, an asymmetric periodic motion can be characterized by a two-parameter unfolding of cusp bifurcation, and a typical symmetric breaking phenomenon takes place during pitchfork bifurcation.