Basins of coexisting multi-dimensional tori in a vibro-impact system

Abstract

Based on the method of Poincare mapping undercellreference,wedescribebasinsofattractionfor coexisting multi-dimensional tori attractors in a three- degree-of-freedom vibro-impact system. Because the multi-dimensional tori attractors are very rare in the low-dimensional systems, we find that these coexist- ing tori attractors have positive measure basins in the sense of Milnor. The coexisting multi-dimensional tori attractors can be distinguished by the exactly Poincare mappingandLyapunovdimension.Thebasinofattrac- tion can be estimated by the limit cycle in the Poincare section from the viewpoint of engineering.