Multiple nested basin boundaries in nonlinear driven oscillators

A special type of basins of attraction for high-period coexisting attractors is investigated, which basin boundaries possess multiple nested structures in a driven oscillator. We analyze the global organization of basins and discuss the mechanism for the appearance of layered structures. The unstable periodic orbits and unstable limit cycle are also detected in the oscillator. The basin organization is governed by the ordering of regular saddles and the regular saddle connections are the interrupted by the unstable limit cycle. Wada basin boundary with different Wada number is discovered. Wada basin boundaries for the hidden and rare attractors are also verified.