Universal mechanism for the intermittent route to strange nonchaotic attractors in quasiperiodically forced systems

To examine the universality for the intermittent route to strange nonchaotic attractors (SNAs), we investigate the quasiperiodically forced Henon map, ring map and Toda oscillator which are high-dimensional invertible systems. In these invertible systems, dynamical transition to an intermittent SNA occurs via a phase-dependent saddle–node bifurcation, when a smooth torus collides with a 'ring-shaped' unstable set. We note that this bifurcation mechanism for the appearance of intermittent SNAs is the same as that found in a simple system of the quasiperiodically forced noninvertible logistic map. Hence, the intermittent route to SNAs seems to be 'universal', in the sense that it occurs through the same mechanism in typical quasiperiodically forced systems of different nature.

[1]  Chang-song Zhou,et al.  Robust communication via synchronization between nonchaotic strange attractors , 1997 .

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

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

[4]  H. Osinga,et al.  Boundary crisis in quasiperiodically forced systems , 2000 .

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

[6]  Ramakrishna Ramaswamy,et al.  Synchronization of strange nonchaotic attractors , 1997, chao-dyn/9709026.

[7]  Kuznetsov,et al.  Experimental observation of dynamics near the torus-doubling terminal critical point , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Bifurcation structure of the Toda oscillator. , 1988, Physical review. A, General physics.

[9]  Sergey P Kuznetsov.  Torus fractalization and intermittency. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Ramakrishna Ramaswamy,et al.  Bifurcations and transitions in the quasiperiodically driven logistic map , 2000 .

[11]  Route to chaos via strange non-chaotic attractors , 1990 .

[12]  Mogens H. Jensen,et al.  Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps , 1984 .

[13]  Grebogi,et al.  Evolution of attractors in quasiperiodically forced systems: From quasiperiodic to strange nonchaotic to chaotic. , 1989, Physical review. A, General physics.

[14]  Morikazu Toda,et al.  Studies of a non-linear lattice , 1975 .

[15]  Werner Meyer-Ilse,et al.  Period doubling and chaotic behavior in a driven Toda oscillator , 1984 .

[16]  J. Yorke,et al.  Strange attractors that are not chaotic , 1984 .

[17]  Ulrike Feudel,et al.  Characterizing strange nonchaotic attractors. , 1995, Chaos.

[18]  A. Dinklage,et al.  OBSERVATION OF A STRANGE NONCHAOTIC ATTRACTOR IN A NEON GLOW DISCHARGE , 1997 .

[19]  Lakshmanan,et al.  Intermittency transitions to strange nonchaotic attractors in a quasiperiodically driven duffing oscillator , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  J. Stark,et al.  Locating bifurcations in quasiperiodically forced systems , 1995 .

[21]  Annette Witt,et al.  Birth of strange nonchaotic attractors due to interior crisis , 1997 .

[22]  Celso Grebogi,et al.  Phase-locking in quasiperiodically forced systems , 1997 .

[23]  Kaneko,et al.  Fractalization of a torus as a strange nonchaotic attractor. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Edward Ott,et al.  Fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Ramakrishna Ramaswamy,et al.  Strange Nonchaotic attractors , 2001, Int. J. Bifurc. Chaos.

[26]  Jukka A. Ketoja,et al.  Harper equation, the dissipative standard map and strange nonchaotic attractors: relationship between an eigenvalue problem and iterated maps , 1997 .

[27]  Hinke M. Osinga,et al.  Multistability and nonsmooth bifurcations in the Quasiperiodically forced Circle Map , 2001, Int. J. Bifurc. Chaos.

[28]  M Lakshmanan,et al.  Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map: mechanisms and their characterizations. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  J. Heagy,et al.  The birth of strange nonchaotic attractors , 1994 .

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

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

[32]  Kuznetsov,et al.  Critical point of tori collision in quasiperiodically forced systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  Sergey P. Kuznetsov,et al.  Renormalization group for scaling at the torus-doubling terminal point , 1998 .

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

[35]  Kuznetsov,et al.  Birth of a strange nonchaotic attractor: A renormalization group analysis. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[37]  Jürgen Kurths,et al.  Strange non-chaotic attractor in a quasiperiodically forced circle map , 1995 .

[38]  Edward Ott,et al.  Mechanism for the intermittent route to strange nonchaotic attractors. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Ott,et al.  Quasiperiodically forced damped pendula and Schrödinger equations with quasiperiodic potentials: Implications of their equivalence. , 1985, Physical review letters.

[40]  B R Hunt,et al.  Fractal properties of robust strange nonchaotic attractors. , 2001, Physical review letters.

[41]  Juergen Kurths,et al.  Multiband strange nonchaotic attractors in quasiperiodically forced systems , 1996 .