Abstract
For the appearance of chaos some typical scenarios, which include the inverted bifurcation, the period-doubling bifurcation, intermittent chaos and a transition from a torus to a strange attractor, have been investigated experimentally and theoretically[1]. Among these scenarios, in particular, a transition of a torus to a strange attractor is of great interest in the study of the connection between chaos in dissipative systems and in conservative systems. In one- and two-dimensional difference systems several important properties have been found. The whole aspect of the scenario, however, seems not yet to be clear.
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References
R.H.G. Helleman in Fundamental Problems in Statistical Physics V, E.G.D. Cohen ed., ( North-Holland,.Amsterdam, 1980 ) p. 165.
T. Shimizu and A. Ichimura, Phys. Letters 91A, 52 (1982).
T. Shimizu, Physica 97A. 383 (1979).
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© 1984 Springer-Verlag Berlin Heidelberg
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Shimizu, T. (1984). Perturbation Theory Analysis of Bifurcations in a Three-Dimensional Differential System. In: Kuramoto, Y. (eds) Chaos and Statistical Methods. Springer Series in Synergetics, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69559-9_13
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DOI: https://doi.org/10.1007/978-3-642-69559-9_13
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