Two characteristics of planar intertwined basins of attraction

In this paper, we investigate the intertwined basins of attraction for planar dynamical systems. We prove that the intertwining property is preserved by topologically equivalent systems. Two necessary and sufficient conditions for a planar system having intertwined basins are given.

► A new mathematical definition of intertwined basins of attraction is proposed.
► Basins are intertwined iff a limit set of stable manifold contains at least two points.
► Basins are intertwined iff the closure of stable manifold is not arc-connected.
► The intertwining property is preserved by topologically equivalent dynamical systems.