Wada bifurcations and partially Wada basin boundaries in a two-dimensional cubic map

The partially Wada basin boundaries are referred to the coexistence of Wada points and non-Wada points in the same basin boundary. We demonstrate two types of Wada bifurcations and analyze the transitions from totally Wada basins to partially Wada basins and from totally Wada basins to totally Wada basins in a two-dimensional cubic map. We describe some numerical experiments giving the evidence of partially Wada basin boundaries. Our results show that the basin cell erosion and the basin cell bifurcation can induce the Wada basin boundary metamorphoses.