Critical behavior of period doublings in coupled inverted pendulums

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 6, 1998, Pages 7231-7242

  Kim, Sang Yoon ^a,b   Hu, Bambi ^b,c  

^a Kangwon National University   (South Korea)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^c University of Houston   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243900620     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.7231     Document Type: Article

References (26)

1. R. V. Buskirk and C. Jeffries, Phys. Rev. A 31, 3332 (1985). PLRAAN
2. P. Hadley and M. R. Beasley, Appl. Phys. Lett. 50, 621 (1987); APPLAB
3. P. Hadley, M. R. Beasley, and K. Wiesenfeld, Phys. Rev. B 38, 8712 (1988). PRBMDO
4. S. H. Strogatz, C. M. Marcus, R. M. Westervelt, and R. E. Mirollo, Physica D 36, 23 (1989). PDNPDT
5. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, New York, 1984).
6. A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, Berlin, 1980).
7. L. D. Landau and E. M. Lifshitz, Mechanics (Pergamon, New York, 1976), p. 80;
8. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978), p. 113.
9. H. C. Corben and P. Stehle, Classical Mechanics, 2nd ed. (Wiley, New York, 1960), p. 67.
10. P. L. Kapitza, in Collected Papers of P. L. Kapitza, edited by D. Ter Haar (Pergamon, London, 1965), p. 714.
11. J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems (Interscience, New York, 1966), p. 189.
12. M. Levi, SIAM (Soc. Ind. Appl. Math.) Rev. 30, 639 (1988). SIREAD
13. S.-Y. Kim and B. Hu, Phys. Rev. E 58, 3028 (1998). PLEEE8
14. M. J. Feigenbaum, J. Stat. Phys. 19, 25 (1978); JSTPBSM.
15. S. Kuznetsov, Radiophys. Quantum Electron. 28, 681 (1985); RPQEACH.
16. Kook, F. H. Ling, and G. Schmidt, Phys. Rev. A 43, 2700 (1991). PLRAAN
17. S.-Y. Kim and H. Kook, Phys. Rev. A 46, R4467 (1992); PLRAANS
18. Y. Kim H. Kook Phys. Lett. A 178, 258 (1993);
19. S.-Y. Kim H. Kook Phys. Rev. E 48, 785 (1993)
20. S. Lefschetz, Differential Equations: Geometric Theory (Dover, New York, 1977), Sec. 3.5.
21. I. Waller and R. Kapral, Phys. Rev. A 30, 2047 (1984). PLRAAN
22. S. Lefschetz, Differential Equations: Geometric Theory (Ref. 15), p. 60. See Eq. (4.3).
23. S.-Y. Kim and B. Hu, Phys. Rev. A 44, 934 (1991); PLRAAN
24. Phys. Rev. A S.-Y. Kim and D.-S. Lee, 45, 5480 (1992).
25. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983), Sec. 3.5.
26. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983), Sec. 5.3.