Chaos, bifurcations and periodic orbits of the Lorenz-Stenflo system

Physica Scripta

Volumn 55, Issue 4, 1997, Pages 394-402

  Zhou, Cangtao ^a   Lai, C H ^a   Yu, M Y ^b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007653981     PISSN: 00318949     EISSN: None     Source Type: Journal    
DOI: 10.1088/0031-8949/55/4/003     Document Type: Article

References (15)

1. Stenflo, L., Physica Scripta 53, 83 (1996).
2. Lorenz, E. N., J. Atmos. Sci. 20, 130 (1963).
3. Haken, H., Phys. Lett. 53A, 77 (1975).
4. Dong, B. and Yeh, K. C., Physica Scripta 43, 534 (1991).
5. See, for example, C. Sparrow "The Lorenz Equations: Bifurcations, Chaos and Strange Attractors" (Springer, New York, 1983).
6. Froyland, J. and Alfsen, K. H., Phys. Rev. A29, 2928 (1984).
7. Alfsen, K. H. and Froyland, J., Physica Scripta 31, 15 (1985).
8. We note that the definitions of the Rayleigh and Prandtl numbers differ somewhat from their usual ones because of rescaling [1].
9. Yu, M. Y. and Yang, B., Physica Scripta 54, 140 (1996).
10. Throughout this paper we set b = 8/3 whenever the numerical value of b is needed.
11. However, we should mention that forward bifurcation may also exist at larger values of the rotational number.
12. Tsonis, A. A., "Chaos: From Theory to Applications" (Plenum, New York, 1992).
13. Feigenbaum, M. J. J., Stat. Phys. 19, 25 (1978).
14. 2n⋯ should appear. The reason that the L-S system does not follow an exact Sarkovskii sequence could be traced to the coexistence of saddle-node and period-doubling bifurcations, which lead to much increased complexity of the periodic orbits. In fact, the sequence of bifurcations of the L-S system cannot be described in terms of a unimodal mapping.
15. Sarkovskii, A. N., Ukranian Math. J. 16, 61 (1964).