Re-entrant hexagons and locked Turing-Hopf fronts in the cima reaction

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 5, 1998, Pages 1003-1012

  Mosekilde, E ^a   Larsen, F ^a   Dewel, G ^b   Borckmans, P ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032066173     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498000814     Document Type: Article

References (30)

1. Bensimon, D., Shraiman, B. I. & Croquette, V. [1988] "Nondiabatic effects in convection," Phys. Rev. A38, 5461-5464.
2. Boehm, J. von & Bak, P. [1979] "Devil's staircase and the commensurate-commensurate transitions in CeSb," Phys. Rev. Lett. 42, 122-125.
3. Bohr, T., Bak, P. & Jensen, M. H. [1984] Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps," Phys. Rev. A30, 1970-1981.
4. Borckmans, P., De Wit, A. & Dewel, G. [1992] "Competition in ramped Turing structures," Physica A188, 137-157.
5. Borckmans, P., Jensen, O., Pannbacker, V. O., Mosekilde, E., Dewel, G. & De Wit, A. [1995] "Localized Turing and Turing-Hopf patterns," in Modeling the Dynamics of Biological Systems, eds. Mosekilde, E. & Mouritsen, O. G. (Springer, Berlin).
6. Castets, V., Dulos, E., Boissonade, J. & De Kepper, P. [1990] "Experimental evidence of sustained standing Turing-type nonequilibrium chemical patterns," Phys. Rev. Lett. 64, 2953-2956.
7. Douglas Jr., J. [1962] "Alternating directions methods for three space variables," Numer. Math. 4, 41-63.
8. Dufiet, V. & Boissonade, J. [1992] "Numerical studies of Turing patterns selection in a two-dimensional system," Physica A188, 158-171.
9. Hilali, M. F., Metens, S., Borckmans, P. & Dewel, G. [1995] "Pattern selection in the generalized Swift-Hohenberg model," Phys. Rev. E51, 2046-2052.
10. Jensen, O., Mosekilde, E., Borckmans, P. & Dewel, G. [1996] "Computer simulations of Turing structures in the chlorite-iodide-malonic acid system,Physica Scripta 53, 243-251.
11. Jensen, O., Pannbacker, V. O., Dewel, G. & Borckmans, P. [1993] "Subcritical transitions to Turing structures," Phys. Lett. A179, 91-96.
12. Jensen, O., Pannbacker, V. O., Mosekilde, E., Dewel, G. & Borckmans, P. [1994] "Localized structures and front propagation in the Lengyel-Epstein model," Phys. Rev. E50, 736-749.
13. Lengyel, I. & Epstein, I. R. [1991] "Modeling of Turing structures in the chlorite-iodide-malonic acid-starch reaction system," Science 251, 650-652.
14. Lengyel, I. & Epstein, I. R. [1992] "A chemical approach to designing Turing patterns in reaction-diffusion systems," Proc. Natl. Acad. Sci. USA 89, 3977-3979.
15. Lengyel, I., Rabai, G. & Epstein, I. R. [1990] "Batch oscillation in the reaction of chlorine dioxide with iodine and malonic acid," J. Am. Chem. Soc. 112 4606-4607.
16. Münster, A. F., Watzl, M. & Schneider, F. W. [1996] "Two-dimensional Turing-like patterns in the PA-MBO system and effects of an electric field," Physica Scripta T67, 58-62.
17. Nicolis, G. & Progogine, I. [1977] Self-Organization in Nonequilibrium Chemical Systems (Wiley, New York).
18. Ouyang, Q., Noszticzius, Z. & Swinney, H. L. [1992] "Spatial bistability of two-dimensional Turing patterns in a reaction-diffusion system," J. Phys. Chem. 96, 6773-6776.
19. Ouyang, Q. & Swinney, H. L. [1991a] "Transition from a uniform state to hexagonal and striped Turing patterns," Nature 352, 610-612.
20. Ouyang, Q. & Swinney, H. L. [1991b] "Transition to chemical turbulence," Chaos 1, 411-420.
21. Pearson, J. E. [1993] "Complex patterns in a simple system," Science 261, 189-192.
22. Perraud, J.-J., De Wit, A., Dulos, E., De Kepper, P., Dewel, G. & Borckmans, P. [1993] "One-dimensional spirals: Novel asynchronous chemical wave sources," Phys. Rev. Lett. 71, 1272-1275.
23. Pismen, L. M. [1980] "Pattern selection at the bifurcation point," J. Chem. Phys. 72, 1900-1907.
24. Rasmussen, K. E., Mazin, W., Mosekilde, E., Dewel, G. & Borckmans, P. [1996] "Wave-splitting in the bistable gray-scott model," Int. J. Bifurcations and Chaos 6, 1077-1092.
25. Rovinsky, A. & Menzinger, M. [1992] "Interaction of Turing and Hopf bifurcations in chemical systems," Phys. Rev. A46, 6315-6322.
26. Rudovics, B., Dulos, E. & De Kepper, P. [1996] "Standard and nonstandard Turing patterns and waves in the CIMA reaction," Physica Scripta T67, 43-50.
27. Skinner, G. S. & Swinney, H. L. [1991] "Periodic to quasiperiodic transition of chemical spiral rotation," Physica D48, 1-16.
28. Thual, O. & Fauve, S. [1988] "Localized structures generated by subcritical instabilities," J. Phys. France 49, 1829-1833.
29. Turing, A. M. [1952] "The chemical basis of morphogenesis," Trans. Roy. Soc. Lond. B327, 37-72.
30. Verdasca, J., De Wit, A., Dewel, G. & Borckmans, P. [1992] "Re-entrant hexagonal Turing structures," Phys. Lett. A168, 194-198.