  This paper focusses attention on the strange nonchaotic attractors (SNA) of a
quasiperiodically forced dynamical system. Several routes, including the
standard ones by which the appearance of strange nonchaotic attractors takes
place, are shown to be realizable in the same model over a two parameters
($f-\epsilon$) domain of the system. In particular, the transition through
torus doubling to chaos via SNA, torus breaking to chaos via SNA and period
doubling bifurcations of fractal torus are demonstrated with the aid of the two
parameter ($f-\epsilon$) phase diagram. More interestingly, in order to
approach the strange nonchaotic attractor, the existence of several new
bifurcations on the torus corresponding to the novel phenomenon of torus
bubbling are described. Particularly, we point out the new routes to chaos,
namely, (1) two frequency quasiperiodicity $\to$ torus doubling $\to$ torus
merging followed by the gradual fractalization of torus to chaos, (2) two
frequency quasiperiodicity $\to$ torus doubling $\to$ wrinkling $\to$ SNA $\to$
chaos $\to$ SNA $\to$ wrinkling $\to$ inverse torus doubling $\to$ torus $\to$
torus bubbles followed by the onset of torus breaking to chaos via SNA or
followed by the onset of torus doubling route to chaos via SNA. The existence
of the strange nonchaotic attractor is confirmed by calculating several
characterizing quantities such as Lyapunov exponents, winding numbers, power
spectral measures and dimensions. The mechanism behind the various bifurcations
are also briefly discussed.
