Strange nonchaotic attractors via torus breakdown

In this paper, we examine the quasiperiodically driven logistic map and discuss a mechanism for the development of strange nonchaotic attractors. It is shown that the attractors can be created from two-frequency torus breakdown. We find that the torus does not undergo period-doubling cascade as usual as system parameters vary, instead, the torus curve becomes extremely wrinkled, loses its smoothness and finally becomes fractal. However the Lyapunov exponent remains negative during the process. The mechanism can be used to explain the onset of strange nonchaotic behaviors in a class of systems.