Kinks and Spatially Complex Behavior in One-Dimensional Coupled Map Lattices
Recent studies on low-dimensional dynamical systems have had great success in elucidating the onset of turbulence and various aspects of chaos . The success, however, is limited to systems with a few number of excited modes. Then, what happens in a system with a large number of excited modes and with a spatial complexity? Can the low-dimensional chaos be an elementary process for the turbulence? Furthermore, spatial patterns are important for the understanding of turbulence. How are the patterns in nonlinear systems characterized? What is the effect of spatial patterns on the onset of chaos?
KeywordsFlat Region Excited Mode Laminar Region Probabilistic Cellular Automaton Kink Position
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- 1.See for recent advances, Chaos and Statistical Methods(ed. Y. Kuramoto, Springer, 1984; Proceeding of the previous Kyoto Summer Institute )Google Scholar
- 6.K. Kaneko, Prog. Theor. Phys. 69(1983) 1427; see also J. M. Yuan, M. Tung, D.H. Feng, L.M. Naruducci, Phys. Rev. A28 (1983) 1662;T. Hogg and B.A. Huberman, Phys. Rev. 29A (1984) 275; see also for the case with N.6, I. Waller and R. Kapral, preprint (1984) submitted to Phys Rev. AGoogle Scholar
- 7.K. Kaneko, Prog. Theor. Phys. 72 (1984) No. 3Google Scholar
- 8.T. Yamada and H. Fujisaka, Prog. Theor. Phys. 70 (1983) 1240 and preprint (1984) to appear in Prog. Theor. Phys.Google Scholar
- 9.Y. Aizawa, preprint (1984) Kyoto Univ.Google Scholar
- 10.M.J. Feigenbaum, J. Stat. Phys. 19 (1978) 25, 21 (1979) 669Google Scholar
- 12.A summary of the recent studies on the transition from torus to chaos can be seen in K. Kaneko, Ph. D. Thesis, Univ. of Tokyo, 1983 (unpublished)Google Scholar
- 13.Y. Pomeau and P. Manneville, Comm. Math. Phys. 74 (1980) 189; see also J.E. Hirsch, B.A. Huberman and D.J. Scalapino, Phys. Rev. A25 (1982) 519Google Scholar
- 15.S. Wolfram, Rev. Mod. Phys. 55 (1983) 601; P. Grassberger, F. Krause, and T. Twer, J. Phys. A17 (1984) L105Google Scholar
- 17.V.M. Alekseev and M.V. Yakobson, Phys. Rep. 75 (1981) 287; see also S. Wolfram, Physica 10D (1984) 1Google Scholar
- 18.C. Grebogi, E. Ott and J. A. Yorke, Phys. Rev. Lett. 51 (1983) 339 and preprint (1984)Google Scholar
- 19.K. Kaneko, Prog. Theor. Phys. 71 (1984) 282 and to appear in Theory of Dynamical Systems and Its Applications to Nonlinear Problems (ed. H. Kawakami, World Sci. Co. Pub.)Google Scholar