Strange nonchaotic attractor in low-frequency quasiperiodically driven systems

To generate strange nonchaotic attractor in quasiperiodically driven systems, there must be an unstable region in its phase-space. In this paper, a theoretical analysis shows that the quasiperiodic force acts as noise to lead the trajectory running into different expanding orbits when the trajectory repeatedly runs into the unstable region. Thus the resulting attractor is strange. The local-phase Lyapunov exponent is introduced for the study of low-frequency quasiperiodically driven systems. It is shown that the local-phase Lyapunov exponents can be approximated by the exponents of autonomous systems. The statistical properties of SNA system driven by low-frequency quasiperiodic force can then be approached by a set of autonomous systems.