Collective dynamics of a weakly coupled electrochemical reaction on an array

Industrial and Engineering Chemistry Research

Volumn 41, Issue 25, 2002, Pages 6363-6374

  Kiss, István Z ^a   Zhai, Yumei ^a   Hudson, John L ^a  

^a University of Virginia   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARRAYS; ELECTROCHEMISTRY; SYNCHRONIZATION;

PHASE SYNCHRONIZATION;

CHEMICAL ENGINEERING;

CHEMICAL REACTION; DYNAMICS; ELECTROCHEMICAL PROCESS;

ARTICLE; CHEMICAL PARAMETERS; CHEMICAL REACTION; DYNAMICS; ELECTROCHEMISTRY; OSCILLATION; OSCILLATOR;

EID: 0037065278     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie0110235     Document Type: Article

References (34)

1. Kuramoto, Y. Chemical Oscillations, Waves and Turbulence; Springer: Berlin, 1984.
2. Lobban, L.; Luss, D. Spatial temperature oscillations during hydrogen oxidation on a nickel foil. J. Phys. Chem. 1989, 93, 6530.
3. Mertens, F.; Imbihl, R.; Mikhailov, A. Breakdown of global coupling in oscillatory chemical reactions. J. Chem. Phys. 1993, 99, 8668.
4. Slinko, M. M.; Ukharskii, A. A.; Jaeger, N. I. Global and nonlocal coupling in oscillating heterogeneous catalytic reactions: The oxidation of CO on zeolite supported palladium. PCCP Phys. Chem. Chem. Phys. 2001, 3, 1015.
5. Middya, U.; Luss, D. Impact of global interactions on patterns in a simple system. J. Chem. Phys. 1994, 100, 6386.
6. Krischer, K. In Modern Aspects of Electrochemistry; Conway, B. E., Bockris, O. M., White, R. E., Eds.; Kluwer Academic/Plenum Press: New York, 1999; Vol. 32, p 1.
7. Mazouz, N.; Krischer, K.; Flätgen, G.; Ertl, G. Synchronization and pattern formation in electrochemical oscillators: Model calculations. J. Phys. Chem. B 1997, 101, 2403.
8. Birzu, A.; Green, B. J.; Otterstedt, R. D.; Jaeger, N. I.; Hudson, J. L. Modelling of spatiotemporal patterns during metal electrodissolution in a cell with a point reference electrode. PCCP Phys. Chem. Chem. Phys. 2000, 2, 2715.
9. Kiss, I. Z.; Wang, W.; Hudson, J. L. Experiments on arrays of globally coupled periodic electrochemical oscillators. J. Phys. Chem. B 1999, 103, 11433.
10. Karantonis, A.; Shiomi, Y.; Nakabayashi, S. Coherence and coupling during oscillatory metal electrodissolution. J. Electroanal. Chem. 2000, 493, 57.
11. Chaté, H.; Lemaitre, A.; Marcq, P.; Manneville, P. Nontrivial collective behavior in extensively chaotic dynamical systems: An update. Physica A 1996, 224, 447.
12. Kaneko, K. Remarks on the mean-field dynamics of networks of chaotic elements. Physica D 1995, 86, 158.
13. Kaneko, K. Globally coupled chaos violates the law of large numbers but not the central limit theorem. Phys. Rev. Lett. 1990, 65, 1391.
14. Perez, G.; Pandolambruschini, C.; Sinha, S.; Cerdeira, H. A. Nonstatistical behavior of coupled optical systems. Phys. Rev. A 1992, 45, 5469.
15. Perez, G.; Cerdeira, H. A. Instabilities and nonstatistical behavior in globally coupled systems. Phys. Rev. A 1992, 46, 7492.
16. Pikovsky, A. S.; Kurths, J. Do globally coupled maps really violate the law of large numbers? Phys. Rev. Lett. 1994, 72, 1644.
17. Brunnet, L.; Chaté, H.; Manneville, P. Long-range order with local chaos in lattices of diffusively coupled ODEs. Physica D 1994, 78, 141.
18. Brunnet, L. G.; Chaté, H. Phase coherence in chaotic oscillatory media. Physica A 1998, 257, 347.
19. Chaté, H.; Manneville, P. Emergence of effective low-dimensional dynamics in the macroscopic behavior of coupled map lattices. Europhys. Lett. 1992, 17, 291.
20. Shibata, T.; Kaneko, K. Heterogeneity-induced order in globally coupled chaotic systems. Europhys. Lett. 1997, 38, 417.
21. Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J. Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 1996, 76, 1804.
22. Pikovsky, A. S.; Rosenblum, M. G.; Kurths, J. Synchronization in a population of globally coupled chaotic oscillators. Europhys. Lett. 1996, 34, 165.
23. Sakaguchi, H. Phase transition in globally coupled Rössler oscillators. Phys. Rev. E 2000, 61, 7212.
24. Kiss, I. Z.; Zhai, Y.; Hudson, J. L. Collective dynamics of chaotic chemical oscillators and the law of large numbers. Phys. Rev. Lett. 2002, 88, 238301.
25. Wang, W.; Kiss, I. Z.; Hudson, J. L. Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. Chaos 2000, 10, 248.
26. Fei, Z.; Hudson, J. L. Chaotic oscillations on arrays of iron electrodes. Ind. Eng. Chem. Res. 1998, 37, 2172.
27. Kiss, I. Z.; Wang, W.; Hudson, J. L. Populations of coupled electrochemical oscillators. Chaos 2002, 12, 252.
28. Lev, O.; Wolffberg, A.; Sheintuch, M.; Pismen, L. M. Bifurcations to periodic and chaotic motions in anodic nickel dissolution. Chem. Eng. Sci. 1988, 43, 1339.
29. Kiss, I. Z.; Wang, W.; Hudson, J. L. Complexity of globally coupled chaotic electrochemical oscillators. PCCP Phys. Chem. Chem. Phys. 2000, 2, 3847.
30. Gábor, D. J. Inst. Electron. Eng. Part 3 1946, 93, 429.
31. Pikovsky, A. S.; Rosenblum, M. G.; Osipov, G. V.; Kurths, J. Phase synchronization of chaotic oscillators by external driving. Physica D 1997, 104, 219.
32. Tass, P.; Rosenblum, M. G.; Weule, J.; Kurths, J.; Pikovsky, A.; Volkmann, J.; Schnitzler, A.; Freund, H. J. Detection of n:m phase locking from noisy data: Application to magnetoencephalography. Phys. Rev. Lett. 1998, 81, 3291.
33. DeShazer, D. J.; Breban, R.; Ott, E.; Roy, R. Detecting phase synchronization in a chaotic laser array. Phys. Rev. Lett. 2001, 87, 044101.
34. Lachaux, J. P.; Rodriguez, E.; Van Quyen, M. L.; Lutz, A.; Martinerie, J.; Varela, F. J. Studying single trials of phase synchronous activity in the brain. Int. J. Bifurcation Chaos 2000, 10, 2429.