Basin boundaries with nested structure in a shallow arch oscillator

The basin boundaries with nested structure are investigated in a shallow arch oscillator. Basin organization is complex yet systematic and it is governed by the ordering of heteroclinic and homoclinic connections of regular saddles. The Wada properties are verified for eight basin boundaries, where five basin boundaries are totally Wada basin boundaries for a given set of parameters. The organization of nested basin boundaries is governed by the order of saddle connections. The term “Wada number” is introduced to describe the nested structure. The partially Wada basin boundaries are investigated by the erodent cells and the remnant cells.