Quasiperiodically driven maps in the low-dissipation limit

Abstract

We study the quasiperiodically driven Hénon and Standard maps in the weak dissipative limit. In the absence of forcing, there are a large number of coexisting periodic attractors. Although chaotic attractors can also be found, these typically have vanishingly small basins of attraction. Quasiperiodic forcing reduces the multistability in the system, and as the bifurcation parameter is varied, strange nonchaotic attractors (SNAs) are created. The attractor basin for SNAs appears to be the largest among those of all coexisting attractors at such a transition.