Boundary of Two Frequency Behaviour in a System of Three Weakly Coupled Electronic Oscillators

Chaos, Solitons and Fractals

Volumn 9, Issue 8, 1998, Pages 1279-1287

  Ashwin, Peter ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; DYNAMICS;

COUPLED OSCILLATORS; SADDLE NODE BIFURCATION;

OSCILLATORS (ELECTRONIC);

EID: 0032131730     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(98)80001-5     Document Type: Article

References (21)

1. Anishchenko, V. S., Safonova, M. A., Feudel, U., Kurths, J., Bifurcation and transition to chaos through three dimensional tori. Intl. J. Bifn. Chaos., 1994, 4, 595-607.
2. Arnol'd, V. I. (ed), Dynamical systems V, Encyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin, 1994.
3. Aronson, D. G., Chory, M. A., Hall, G. R., McGeehee, R. P., Bifurcations from an invariant circle for two-parameter families of maps of the plaine: a computer-assisted study. Commun. Math. Phys., 1982, 83, 303-354.
4. Arrowsmith, D. K. and Place, C. M., An Introduction to Dynamical Systems. C.U.P., Cambridge, 1990.
5. Ashwin, P., Guaschi, J., Phelps, J. M., Rotation sets and mode locking in an electronic three oscillator system. Physica D, 1993, 66, 392-411.
6. Ashwin, P., Swift, J. W., Unfolding the torus: oscillator geometry from time delays. Journal of Nonlinear Science, 1993, 3, 459-475.
7. Ashwin, P., Swift, J. W., Measuring rotation sets of weakly coupled oscillators. Nonlinearity, 1993, 7, 925-942.
8. Ashwin, P., Swift, J. W., Torus doubling in four weakly coupled oscillators. Intl. J. Bifn. Chaos, 1995, 5, 231-241.
9. Baesens, C., Guckenheimer, J., Kim, S., MacKay, R. S., Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos. Physica D, 1991, 49, 387-475.
10. Battelino, P., Persistence of three-frequency quasiperiodicity under large perturbations. Phys. Rev. A, 1989, 38, 1495-1502.
11. Battelino, P. M., Grebogi, C., Ott, E., Yorke, J. A., Chaotic attractors on a 3-torus, and torus break-up. Physica D, 1989, 39, 299-314.
12. Broer, H. W., Huitema, G. B., Takens, F., Braaksma, B. L. J., Unfoldings and bifurcations of quasi-periodic tori. Memoirs Am. Math. Soc., 1990, 83(421).
13. Chenciner, A., Bifurcation de points fixes elliptiques III, orbites periodiques de petites periodes et elimination resonante des couples de courbes invariantes. Publ. Math. IHES, 1986, 66, 5-91.
14. Feudel, U., Kurths, J., Pikovsky, A. S., Strange nonchaotic attractor in a quasiperiodically forced circle map. Physica D, 1995, 176-186.
15. Galkin, O. G., Phase-locking for dynamical systems on the torus and perturbation theory for Mathieu-type problems. J. Nonlinear Sci., 1994, 4, 127-156.
16. Grebogi, C., Ott, E., Yorke, J. A., Attractors on an N torus: quasiperiodicity versus chaos. Physica D, 1985, 15, 354-373.
17. Iooss, G., Los, J. E., Quasi-genericity of bifurcations to high dimensional invariant tori for maps. Commun. Math. Phys., 1988, 119, 453-500.
18. Linsay, P. S., Cumming, A. W., Three-frequency quasiperiodicity, phase locking and the onset of chaos. Physica D, 1989, 40, 196-217.
19. 3 and doubling bifurcation. Nonlinearity, 1989, 2, 149-174.
20. Lochak, P and Meunier, C., Multiphase averaging for classical systems. App. Math. Sci., Vol. 72, 1988, Springer-Verlag.
21. Poeschel, J., Integrability of Hamiltonian systems on Cantor sets. Comm. Pure Appl. Math., 1982, 35, 653-696.