Abstract
We extend the trajectory scaling function as defined for maps to flows whose dynamics is governed by ordinary differential equations. The results are obtained for the Duffing oscillator and are expected to be the same for other dissipative flows as well.
This is a preview of subscription content, log in via an institution to check access.
References
M. J. Feigenbaum,J. Stat. Phys. 19:25 (1978);21:669 (1979).
M. J. Feigenbaum, L. P. Kadanoff, and S. J. Shenker,Physica 5D:370 (1982); D. A. Rand, S. Ostlund, J. Sethna, and E. D. Siggia,Physica 8D:303 (1983).
H. G. E. Hentschel and I. Procaccia,Physica 8D:435 (1983); P. Grassberger,Phys. Lett. 97A:227 (1983).
T. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Schraiman,Phys. Rev. A 33:1141 (1986).
M. J. Feigenbaum,Physica 7D:16 (1983).
M. J. Feigenbaum,Commun. Math. Phys. 77:65 (1980).
A. L. Belmont, M. J. Vinson, J. A. Glazier, G. H. Gunaratne, and B. G. Kenny,Phys. Rev. Lett. 61:539 (1988).
J. Stoer and R. Bulirsh,Introduction to Numerical Analysis (Springer, New York, 1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
de Sousa Vieira, M.C., Gunaratne, G.H. The trajectory scaling function for period doubling bifurcations in flows. J Stat Phys 58, 1245–1256 (1990). https://doi.org/10.1007/BF01026575
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01026575