Birth of strange nonchaotic attractors through type III intermittency

Abstract A new route and the associated mechanism are described for the creation of a strange nonchaotic attractor during the transition from two-frequency quasiperiodicity to a chaotic attractor through torus doubling bifurcation in quasiperiodically forced systems. The strange nonchaotic attractor arises when a a torus doubled attractor is interrupted by a subharmonic bifurcation, resulting in the inhibition of torus doubling sequence. This transition is shown to exhibit type III intermittent characteristic scaling behaviour. The scenario and mechanism are illustrated in detail through experimental and numerical studies of a quasiperiodically driven simple piecewise linear electronic circuit.

[1]  Ott,et al.  Experimental observation of a strange nonchaotic attractor. , 1990, Physical review letters.

[2]  Grebogi,et al.  Critical exponents for crisis-induced intermittency. , 1987, Physical review. A, General physics.

[3]  Ott,et al.  Strange nonchaotic attractors of the damped pendulum with quasiperiodic forcing. , 1987, Physical review. A, General physics.

[4]  Leon O. Chua,et al.  Strange Nonchaotic Trajectories on Torus , 1997 .

[5]  Kapitaniak.  Generating strange nonchaotic trajectories. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  Leon O. Chua,et al.  BIFURCATION AND CHAOS IN THE SIMPLEST DISSIPATIVE NON-AUTONOMOUS CIRCUIT , 1994 .

[7]  Lai,et al.  Blowout Bifurcation Route to Strange Nonchaotic Attractors. , 1996, Physical review letters.

[8]  Ramakrishna Ramaswamy,et al.  STRANGE NONCHAOTIC ATTRACTORS IN THE QUASIPERIODICALLY FORCED LOGISTIC MAP , 1997, chao-dyn/9711009.

[9]  W. Ditto,et al.  Dynamics of a two-frequency parametrically driven duffing oscillator , 1991 .

[10]  Bulsara,et al.  Observation of a strange nonchaotic attractor in a multistable potential. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[11]  Ramakrishna Ramaswamy,et al.  Intermittency Route to Strange Nonchaotic Attractors , 1997 .

[12]  Ta-lun Yang,et al.  Experimental results of strange nonchaotic phenomenon in a second-order quasi-periodically forced electronic circuit , 1997 .

[13]  Y. Pomeau,et al.  Intermittent transition to turbulence in dissipative dynamical systems , 1980 .

[14]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .

[15]  M. Lakshmanan,et al.  Different routes to chaos via strange nonchaotic attractors in a quasiperiodically forced system , 1998, chao-dyn/9806008.