Circle maps and the devil's staircase in a periodically perturbed oregonator

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 7, Issue 11, 1997, Pages 2621-2628

  Brøns, Morten ^a   Gross, Peter ^b   Bar Eli, Kedma ^c  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b AALBORG UNIVERSITY   (Denmark)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010464396     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001783     Document Type: Article

References (15)

1. Bar-Eli, K. & Brøns, M. [1990] "On period lengthening near the end of oscillations in chemical systems," J. Phys. Chem. 94, 7170-7177.
2. Cvitanović, P., Shraiman, B. & Söderberg, B. [1985] "Scaling laws for mode lockings in circle maps," Physica Scripta 32, 263-270.
3. de Melo, W. & van Strien, S. [1983] One-Dimensional Dynamics (Springer-Verlag, Berlin).
4. Ecke, R. E., Farmer, J. D. & Umberger, D. K. [1989] "Scaling of the Arnold tounges," Nonlinearity 2(2), 175-196.
5. Graczyk, J. [1991] "Harmonic scaling for smooth diffeomorphisms of the circle," Nonlinearity 4, 935-959.
6. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York).
7. Hale, J. K. [1969] Ordinary Differential Equations (Wiley-Interscience, New York).
8. Hockett, K. & Holmes, P. [1988] "Bifurcation to badly orded orbits in one-parameter families of circle maps or angles fallen from the Devil's Staircase," Proc. Am. Math. Soc. 102, 1031-1051.
9. Jonker, L. B. [1990] "The scaling of Arnol'd tounges for differentiable homeomorphisms of the circle," Commun. Math. Phys. 129, 1-25.
10. Kaas-Petersen, C. & Scott, S. K. [1988] "Homoclinic orbits in a simple chemical model of an autocatalytic reaction," Physica D32, 461-470.
11. Markman, G. & Bar-Eli, K. [1994a] "Periodic perturbations of an oscillatory chemical system," J. Phys. Chem. 98, 12248-12254.
12. Markman, G. & Bar-Eli, K. [1994b] "Periodic perturbations of an oscillatory chemical system," in 3rd Int. Symp. Far from Equilibrium Dynamics of Chemical Systems, eds. Gorecki, J., Cukrovski, A. S., Kawczynski, A. L. & Nowakowski, B. (World Scientific, Singapore), pp. 11-36.
13. Maselko, J. & Swinney, H. L. [1986] "Complex periodic oscillations and Farey arithmetic in the Belousov-Zhabotinskii reaction," J. Phys. Chem. 85(11), 6430-6441.
14. Maselko, J. & Swinney, H. L. [1987] "A Farey triangle in the Belousov-Zhabotinskii reaction," Phys. Lett. A119(8), 403-406.
15. Zeng, W.-Z. & Glass, L. [1989] "Symbolic dynamics and skeletons of circle maps," Physica D40, 218-234.