DIFFERENT ROUTES TO CHAOS VIA STRANGE NONCHAOTIC ATTRACTORS IN A QUASI-PERIODICALLY FORCED SYSTEM

This paper focuses attention on the strange nonchaotic attractors (SNA s) of a quasiperiodically forced dynamical system. Several routes, inc luding the standard ones by which the strange nonchaotic attractors ap pear, are shown to be realizable in the same model over a two-paramete r f-epsilon domain of the system. In particular, the transition throug h torus doubling to chaos via SNAs, torus breaking to chaos via SNAs a nd period doubling bifurcations of the fractal torus are demonstrated with the aid of the two-parameter f-epsilon phase diagram. More intere stingly, in order to approach the strange nonchaotic attractor, the ex istence of several bifurcations on the torus corresponding to the hith erto unreported phenomenon of torus bubbling are described. Particular ly, we point out the new routes to chaos, namely, (i) two-frequency qu asiperiodicity-->torus doubling-->torus merging followed by the gradua l fractalization of torus to chaos, and (ii) two-frequency quasiperiod icity-->torus rinkling-->SNA-->chaos-->SNA-->wrinkling-->inverse torus doubling-->torus-->torus bubbles followed by the onset of torus break ing to chaos via SNA or followed by the onset of torus doubling route to chaos via SNAs. The existence of the strange nonchaotic attractor i s confirmed by calculating several characterizing quantities such as L yapunov exponents, winding numbers, power spectral measures, and dimen sions. The mechanism behind the various bifurcations are also briefly discussed.