Strange nonchaotic attractors with Wada basins

• We verify the abundance of strange nonchaotic attractors (SNAs) with Wada basins.
• The routes to the creation of SNAs with Wada basins (SNAsWB) are described.
• The topological structure of SNAs’ Wada basins are identified.
• We investigate the mechanism for the abundance of SNAsWB.
• The SNAs cannot be predicted for the initial conditions on Wada basin boundaries.

We demonstrate strange nonchaotic attractors with Wada basins (SNAsWB), and verify the abundance of SNAsWB in a quasiperiodically forced Holmes map. We identify the routes to the creation of the SNAsWB in a two-parameter space. The SNAsWB are characterized by the maximal Lyapunov exponent, by the estimation of the phase sensitivity exponent, and by the singular-continuous spectra. We observe that the SNAs’ basins are totally Wada basins in a large range of parameters. The topological structures of the SNAs’ Wada basins are distinguished by the basin cell method. We investigate the underlying mechanism for the abundance of SNAsWB, which is responsible for different types of basin cell in the absence of forcing. This suggests that the SNAs cannot be predicted reliably for specific initial conditions. These SNAsWB can thus be expected to occur more commonly in dynamical systems.