Strange attractors of infinitesimal widths in the bifurcation diagram with an unusual mechanism of onset: Nonlinear dynamics in coupled fuzzy control systems. II

Physica D: Nonlinear Phenomena

Volumn 111, Issue 1-4, 1998, Pages 51-80

  Tomonaga, Yuri ^a   Takatsuka, Kazuo ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Bifurcation; Chaos; Fuzzy control; Nonlinear dynamics; Strange attractor

Indexed keywords

EID: 17044403190     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)80005-X     Document Type: Article

References (48)

1. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983);
2. J.M.T. Thompson and H.B. Stewart, Nonlinear Dynamics and Chaos (Wiley, New York, 1986);
3. S. Wiggins, Global and Bifurcations and Chaos (Springer, New York, 1988);
4. R.Z. Sagdeev, D.A. Usikov and G.M. Zaslavsky, Nonlinear Physics (Harwood, Chur, Switzerland, 1988);
5. J. Hale and H. Koçak, Dynamical and Bifurcations (Springer, New York, 1991).
6. T. Matsumoto, M. Komuro, H. Kokubu and R. Tokunaga, Bifurcations (Springer, Berlin, 1993).
7. H.G. Schuster, Deterministic Chaos (VCH, Weinheim, Germany, 1988);
8. A.J. Lichtenberg and M.A. Lieberman, Regular and Chaotic Dynamics (Springer, Berlin, 1992);
9. F.C. Moon, Chaotic and Fractal Dynamics (Wiley, New York, 1992);
10. L.E. Reichl, The Transition to Chaos (Springer, Berlin, 1992).
11. M.J. Feigenbaum, J. Stat. Phys. 19 (1978) 25;
12. M.J. Feigenbaum, J. Stat. Phys. 21 (1979) 669.
13. P. Manneville and Y. Pomeau, Phys. Lett. A 75 (1979) 1;
14. Physica D 1 (1980) 219;
15. Y. Pomeau and P. Manneville, Comm. Math. Phys. 74 (1980) 189.
16. D. Ruelle and F. Takens, Comm. Math. Phys. 20 (1970) 167;
17. S. Newhouse, D. Ruelle and F. Takens, Comm. Math. Phys. 64 (1978) 35;
18. C. Grebogi, E. Ott and J.A. Yorke, Physica D 15 (1985) 354.
19. K. Kaneko, Prog. Theor. Phys. 69 (1983) 1427.
20. T. Matsumoto, L.O. Chua and R. Tokunaga, IEEE Trans. Circuits Syst. Cas-34 (1987) 240.
21. T Kapitaniak, E. Ponce and J. Wojewoda, J. Phys. A 23 (1990) L383.
22. K. Takatsuka, Physica D 82 (1995) 95.
23. P. Bak, T. Bohr and M.H. Jensen, Phys. Rev. A 30 (1984) 319;
24. T. Bohr, P. Bak and M.H. Jensen, Phys. Rev. A 30 (1984) 329;
25. P. Bak, T. Bohr and M.H. Jensen, Phys. Scr. T 9 (1985) 50.
26. B.V. Chirikov, Phys. Rep. 52 (1979) 265.
27. T. Konishi and K. Kaneko, J. Phys. A 25 (1992) 6283.
28. M. Sugeno, Inform. Sci. 36 (1985) 59.
29. L.A. Zadeh, Inform. Control 8 (1965) 338.
30. R. Abraham and J.E. Marsden, Foundations of Mechanics (Addison-Wesley, New York, 1978).
31. G. Benettin, L. Galgani and J.M. Strelcyn, Phys. Rev. A 14 (1976) 2338.
32. R. Shaw, Z. Naturforsch A 36 (1981) 80.
33. C. Grebogi, E. Ott and J.A. Yorke, Phys. Rev. 48 (1982) 1507;
34. C. Grebogi, E. Ott and J.A. Yorke, Physica D 7 (1983) 181;
35. C. Grebogi, E. Ott, F. Romeiras and J.A. Yorke, Phys. Rev. A 36 (1987) 5365.
36. R.H. Abraham and H.B. Stewart, Physica D 21 (1986) 394.
37. Y. Tomonaga and K. Takatsuka, to be published.
38. K. Kaneko, Prog. Theor. Phys. 69 (1983) 403.
39. B. Braaksma, J. Grasman, Physica D 68 (1993) 265.
40. W. Chin, E. Ott, H.E. Nusse and C. Grebogi, Phys. Rev. E 50 (1994) 4427;
41. Phys. Lett. A 201 (1995) 197.
42. G.I. Sánchez-Qrtiz and A.L. Salas-Brito, Physica D 89 (1995) 151;
43. Phys. Lett. A 203 (1995) 300.
44. U. Parlitz and W. Lauterborn, Phys. Rev. A 36 (1987) 242.
45. K. Takatsuka, Bull. Chem. Soc. 66 (1993) 3189.
46. T.Y. Li and J.A. Yorke, Am. Math. Monthly 82 (1975) 985.
47. C. Grebogi, E. Ott, S. Pelikan and J.A. Yorke, Physica D 13 (1984) 261.
48. H-W. Yin, J-H. Dai and H-J. Zhang, Phys. Lett. A 206 (1995) 370.