Bifurcations and strange nonchaotic attractors in a phase oscillator model of glacial-interglacial cycles

Physica D: Nonlinear Phenomena

Volumn 306, Issue , 2015, Pages 25-33

  Mitsui, Takahito ^a   Crucifix, Michel ^a   Aihara, Kazuyuki ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

Author keywords

Glacial interglacial cycles; Ice age; Middle Pleistocene transition; Nonsmooth saddle node bifurcations; Quasiperiodically forced dynamical systems; SNA; Strange nonchaotic attractor

Indexed keywords

DYNAMICAL SYSTEMS; GLACIAL GEOLOGY; GREENHOUSE GASES; INCIDENT SOLAR RADIATION; LOCKS (FASTENERS); OSCILLATORS (MECHANICAL); SALINITY MEASUREMENT;

GLACIAL-INTERGLACIAL CYCLES; ICE AGE; MIDDLE PLEISTOCENE; SADDLE NODE BIFURCATION; STRANGE NONCHAOTIC ATTRACTORS;

BIFURCATION (MATHEMATICS);

EID: 84930684250     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2015.05.007     Document Type: Article

References (61)

1. D. Paillard Quaternary glaciations: from observations to theories Quat. Sci. Rev. 107 2015 11
2. J. Imbrie, E.A. Boyle, S.C. Clemens, A. Duffy, W.E. Howard, G. Kukla, J. Kutzbach, D.G. Martinson, A. McIntyre, A.C. Mix, B. Molfino, J.J. Morley, L.C. Peterson, N.G. Pisias, W.L. Prell, M.E. Raymo, N.J. Shackleton, and J.R. Toggweiler On the structure and origin of major glaciation cycles. 1. Linear responses to Milankovitch forcing Paleoceanography 7 1992 701
3. J. Imbrie, A. Berger, E.A. Boyle, S.C. Clemens, A. Duffy, W.E. Howard, G. Kukla, J. Kutzbach, D.G. Martinson, A. McIntyre, A.C. Mix, B. Molfino, J.J. Morley, L.C. Peterson, N.G. Pisias, W.L. Prell, M.E. Raymo, N.J. Shackleton, J.R. Toggweiler, Paleoceanography, On the structure and origin of major glaciation cycles. 2. The 100,000-year cycle, 8, 699 (1993).
4. W.F. Ruddiman Orbital insolation, ice volume, and greenhouse gases Quat. Sci. Rev. 22 2003 1597
5. δ 18O records Paleoceanography 20 2005 PA1003
6. 2 Quat. Sci. Rev. 25 2006 3150
7. J.D. Hays, J. Imbrie, and N.J. Shackleton Variations in the Earth's orbit: Pacemakers of the ice ages Science 194 1976 1121
8. L. Lisiecki Links between eccentricity forcing and the 100,000-year glacial cycle Nat. Geosci. 3 2010 349
9. J. Nie, J. King, and X. Fang Late Pliocene-early Pleistocene 100-ka problem Geophys. Res. Lett. 35 2008 L21606
10. J.A. Rial, J. Oh, and E. Reischmann Synchronization of the climate systemto eccentricity forcing and the 100,000-year problem Nat. Geosci. 6 2013 289
11. A.L. Berger Long-term variations of daily insolation and Quaternary climatic change J. Atmospheric Sci. 35 1978 2362
12. A. Berger, and M.F. Loutre Insolation values for the climate of the last 10 million years Quat. Sci. Rev. 10 1991 297
13. M. Milankovitch Kanon der Erdbestrahlung und Seine Anwendung auf das Eiszeitenproblem 1941 Königlich Serbische Akademie Belgrade
14. A. Abe-Ouchi, F. Saito, K. Kawamura, M.E. Raymo, J. Okuno, K. Takahashi, and H. Blatter Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume Nature 500 2013 190
15. M. Claussen, L.A. Mysak, A.J. Weaver, M. Crucifx, T. Fichefet, M.-F. Loutre, S.L. Weber, J. Alcamo, V.A. Alexeev, A. Berger, R. Calov, A. Ganopolski, H. Goosse, G. Lohmann, F. Lunkeit, I.I. Mokhov, V. Petoukhov, P. Stone, and Z. Wang Earth system models of intermediate complexity: closing the gap in the spectrum of climate system models Clim. Dynam. 18 2002 579
16. 2 variation J. Geophys. Res. 97 1992 15713
17. A. Ganopolski, R. Calov, and M. Claussen Simulation of the last glacial cycle with a coupled climate ice-sheet model of intermediate complexity Clim. Past 6 2010 229
18. M. Crucifix Traditional and novel approaches to palaeoclimate modelling Quat. Sci. Rev. 57 2012 1
19. M. Ghil, and S. Childress Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics Applied Mathematical Sciences vol. 60 1987 Springer Berlin, Germany
20. B. Saltzman Dynamical Paleoclimatology: Generalized Theory of Global Climate Change International Geophysics vol. 80 2001 Academic Press New York, NY International Geophysics Series
21. J. Weertman Milankovitch solar radiation variations and ice age ice sheet sizes Nature 261 1976 17
22. J. Oerlemans Glacial cycles and ice-sheet modelling Clim. Change 4 1982 353
23. E. Tziperman, M.E. Raymo, P. Huybers, and C. Wunsch Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing Paleoceanography 21 2006 PA4206
24. A.M. Hogg Glacial cycles and carbon dioxide: A conceptual model Geophys. Res. Lett. 35 2008 L01701
25. M. Crucifix Oscillators and relaxation phenomena in Pleistocene climate theory Philos. Trans. R. Soc. A 370 2012 1140
26. B. De Saedeleer, M. Crucifix, and S. Wieczorek Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study Clim. Dyn. 40 2013 273
27. T. Mitsui, and K. Aihara Dynamics between order and chaos in conceptual models of glacial cycles Clim. Dyn. 42 2014 3087
28. M. Crucifix Why could ice ages be unpredictable? Clim. Past 9 2013 2253
29. I. Daruka, P.D. Ditlevsen, A conceptual model for glacial cycles and the middle Pleistocene transition, Clim. Dyn. http://dx.doi.org/10.1007/s00382-015-2564-7 in press.
30. Y. Ashkenazy, and E. Tziperman Are the 41 kyr glacial oscillations a linear response to Milankovitch forcing? Quat. Sci. Rev. 23 2004 1879
31. C. Grebogi, E. Ott, S. Pelikan, and J.A. Yorke Strange attractors that are not chaotic Physica D 13 1984 261
32. K. Kaneko Fractalization of torus Progr. Theoret. Phys. 71 1984 1112
33. A. Prasad, S.S. Negi, and R. Ramaswamy Strange nonchaotic attractors Internat. J. Bifur. Chaos Appl. Sci. Engrg. 11 2001 291
34. U. Feudel, S. Kuznetsov, and A. Pikovsky Strange Nonchaotic Attractors 2006 World Scientific Singapore
35. R. Ramaswamy Synchronization of strange nonchaotic attractors Phys. Rev. E 56 1997 7294
36. S. Uennohara, T. Mitsui, Y. Hirata, T. Morie, Y. Horio, and K. Aihara Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency Chaos 23 2013 023110
37. A. Pikovsky, and U. Feudel Characterizing strange nonchaotic attractors Chaos 5 1995 253
38. U. Feudel, J. Kurths, and A. Pikovsky Strange non-chaotic attractor in a quasiperiodically forced circle map Physica D 88 1995 176
39. P. Glendinning, T.H. Jäger, and G. Keller How chaotic are strange nonchaotic attractors? Nonlinearity 19 2006 2005
40. T. Mitsui Subdiffusion due to strange nonchaotic dynamics: A numerical study Phys. Rev. E 83 2011 066212
41. T. Nishikawa, and K. Kaneko Fractalization of a torus as a strange nonchaotic attractor Phys. Rev. E 54 1996 6114
42. W. Ditto, M. Spano, H. Savage, S. Rauseo, J. Heagy, and E. Ott Experimental observation of a strange nonchaotic attractor Phys. Rev. Lett. 65 1990 533
43. T. Zhou, F. Moss, and A. Bulsara Observation of a strange nonchaotic attractor in a multistable potential Phys. Rev. A 45 1992 5394
44. T. Yang, and K. Bilimgut Experimental results of strange nonchaotic phenomenon in a second-order quasi-periodically forced electronic circuit Phys. Lett. A 236 1997 494
45. K. Thamilmaran, D. Senthilkumar, A. Venkatesan, and M. Lakshmanan Experimental realization of strange nonchaotic attractors in a quasiperiodically forced electronic circuit Phys. Rev. E 74 2006 036205
46. G. Ruiz, and P. Parmananda Experimental observation of strange non-chaotic attractors in a driven excitable system Phys. Lett. A 367 2007 478
47. T. Mitsui, S. Uenohara, T. Morie, Y. Horio, and K. Aihara Torus-doubling process via strange nonchaotic attractors Phys. Lett. A 376 2012 1907
48. J.F. Lindner, V. Kohar, B. Kia, M. Hippke, J.G. Learned, and W.L. Ditto Strange nonchaotic stars Phys. Rev. Lett. 114 2015 054101
49. N.N. Ivashchenko, V.M. Kotlyakov, D.M. Sonechkin, N.V. Vakulenko, On bifurcations inducing glacial cycle lengthening during Pliocene/Pleistocene epoch, 24, 1440018 (2014).
50. Y. Kuramoto Chemical Oscillations, Waves, and Turbulence 1984 Springer Berlin
51. A. Bondeson, E. Ott, and T.M. Antonsen Quasiperiodically forced damped pendula and Schrödinger equation with quasiperiodic potentials: Implication of their equivalence Phys. Rev. Lett. 55 1985 2103
52. F.J. Romeiras, A. Bondeson, E. Ott, T.M. Antonsen Jr., and C. Grebogi Quasiperiodically forced dynamical systems with strange nonchaotic attractors Physica D 26 1987 277
53. E. Neumann, and A. Pikovsky Quasiperiodically driven Josephson junctions: strange nonchaotic attractors, symmetries and transport Eur. Phys. J. B 26 2002 219
54. S.P. Kuznetsov, and E. Neumann Torus fractalization and singularities in the current-voltage characteristics for the quasiperiodically forced Josephson junction Europhys. Lett. 61 2003 20
55. K. Bjerklöv, and T. Jäger Rotation numbers for quasiperiodically forced circle maps - mode-locking vs. strict monotonicity J. Amer. Math. Soc. 22 2008 353
56. U. Feudel, C. Grebogi, and E. Ott Phase-locking in quasiperiodically forced systems Phys. Rep. 290 1997 11
57. T. Jäger The creation of strange non-chaotic attractors in non-smooth saddle-node bifurcations Mem. Am. Math. Soc. 945 2009 1
58. À. Haro, and J. Puig Strange non-chaotic attractors in Harper maps Chaos 16 2006 033127
59. A. Ganopolski, and R. Calov The role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles Clim. Past 7 2011 1415
60. B. Saltzman, and K.A. Maasch A first-order global model of late Cenozoic climatic change Trans. R. Soc. Edinb. Earth Sci. 81 1990 315
61. T. Mitsui, M. Crucifix, Effects of noise on the dynamics of glacial cycles, submitted for publication.