Quick Search:
Prog. Theor. Phys. Vol. 76 No. 1 (1986) pp. 302-304
Letters
Oscillations of Torus and Collision Torus-Chaos in a Delayed Circle Map
Claudio Franciosi
Istituto di Scienza delle Costruzioni, Facoltà di Ingegneria, Università di Napoli, 80125 Napoli
(Received December 23, 1985)
Abstract:
A delayed version of the well-known circle map is examined, and a particular interesting scenario is closely followed. Oscillations of tori can be observed, according to an already explained mechanism, and a global bifurcation with hysteresis is illustrated, in which a strange attractor is suddenly destroyed by colliding with a coexisting saddle object. First numerical comparisons in the parameter plane with the circle map are also given.
URL :
http://ptp.ipap.jp/link?PTP/76/302/
DOI : 10.1143/PTP.76.302
References:
-
L. Glass, M. Guevara, A. Shrier and R. Perez, Physica 7D (1983), 89[Elsevier].
-
J. Belair and L. Glass, Physica 16D (1985), 143[Elsevier].
- V. I. Arnord, Geometrical Methods in the Theory of Ordinary Differential Equations (Springer Verlag, 1983).
- M. R. Herman, Publ. IHES Vol. 49 (1980), 1; ibid. Vol. 49 (1980), 239.
-
M. J. Feigenbaum, L. P. Kadanoff and S. J. Shenker, Physica 5D (1982), 370[Elsevier].
-
S. Ostlund, D. A. Rand, J. Sethna and E. Siggia, Physica 8D (1983), 303[Elsevier].
-
S. J. Shenker, Physica 5D (1982), 405[Elsevier].
- H. Daido, Prog. Theor. Phys. 68 (1982), 1935[PTP].
- K. Kaneko, Prog. Theor. Phys. 68 (1982), 669[PTP].
- K. Kaneko, Prog. Theor. Phys. 72 (1984), 1089[PTP].
- S. N. Coppersmith and H. B. Stewart, to be published.
- J. Neimark, Dokl. Akad. Nauk SSSR (1959), 736.
- J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dymanical Systems and Bifurcations of Vector Fields (Springer Verlag, 1983).
- K. Kaneko, Prog. Theor. Phys. 72 (1984), 202[PTP].
- J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos (Wiley, Chichester, 1986 to appear).