Route to chaos via strange non-chaotic attractors by reshaping periodic excitations

We present theoretical and numerical evidence for a new route, strange nonchaotic behavior <--> chaos, in two-period quasiperiodically driven dynamical systems by solely changing the excitation waveform. A characteristic signature of this route is the existence of a sequence of intervals over a wide range of waveforms for which only strange non-chaotic attractors or chaos appear, alternatingly. We also found that the largest nontrivial Lyapunov exponent passes through zero linearly near each transition point, which confirms and extends the scaling behavior previously reported for other control parameters.