Excitatory and inhibitory coupling in a one-dimensional array of Belousov-Zhabotinsky micro-oscillators: Theory

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 6, 2011, Pages

  Vanag, Vladimir K ^a   Epstein, Irving R ^a  

^a BRANDEIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTIPHASE OSCILLATIONS; AQUEOUS DROPLETS; BELOUSOV-ZHABOTINSKY REACTIONS; COMPLEX BEHAVIOR; COUPLING STRENGTHS; EXCITATORY COUPLING; GAP SIZE; IN-PHASE OSCILLATIONS; INHIBITORY COUPLING; MALONIC ACID; OIL PHASE; ONE-DIMENSIONAL ARRAYS; PARTITION COEFFICIENT; SPATIOTEMPORAL PATTERNS; TURING PATTERNS;

BEHAVIORAL RESEARCH; CARBOXYLIC ACIDS;

DROPS;

EID: 84855303459     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.066209     Document Type: Article

References (36)

1. I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics (Oxford University Press, New York, 1998).
2. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001).
3. S. H. Strogatz and I. Stewart, Sci. Am. SCAMAC 0036-8733 10.1038/scientificamerican1293-102 269, 102 (1993).
4. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
5. S. Boccaletti, Phys. Rep. 10.1016/S0370-1573(02)00137-0 366, 1 (2002).
6. V. S. Afraimovich, V. I. Nekorkin, G. V. Osipov, and V. D. Shalfeev, Stability, Structures and Chaos in Nonlinear Synchronization Network, Vol. 31 (World Scientific, Singapore, 1995).
7. R. Dilão, Chaos CHAOEH 1054-1500 10.1063/1.3139117 19, 023118 (2009).
8. E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (MIT Press, Cambridge, 2007).
9. A. Camilli and B. L. Bassler, Science SCIEAS 0036-8075 10.1126/science.1121357 311, 1113 (2006).
10. A. F. Taylor, Science SCIEAS 0036-8075 10.1126/science.1166253 323, 614 (2009).
11. M. N. Stolyarov, V. A. Romanov, and E. I. Volkov, Phys. Rev. E 1539-3755 10.1103/PhysRevE.54.163 54, 163 (1996).
12. E. I. Volkov and D. V. Volkov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.046232 65, 046232 (2002). (Pubitemid 40618980)
13. M. Toiya, V. K. Vanag, and I. R. Epstein, Angew. Chem. Int. Ed. 1433-7851 10.1002/anie.200802339 47, 7753 (2008).
14. S. Thutupalli, S. Herminghaus, and R. Seemann, Soft Matter 1744-683X 10.1039/c0sm00312c 7, 1312 (2011).
15. B. P. Belousov, in Collection of Short Papers on Radiation Medicine (Medgiz, Moscow, 1959), p. 145.
16. A. M. Zhabotinsky, Proc. Acad. Sci. USSR 157, 392 (1964).
17. M. Toiya, J. Phys. Chem. Lett. 1948-7185 10.1021/jz100238u 1, 1241 (2010).
18. J. J. Delgado (to be published).
19. FlexPDE, http://www.pdesolutions.com (2010).
20. V. K. Vanag and I. R. Epstein, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.066213 81, 066213 (2010).
21. R. J. Field and R. M. Noyes, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1681288 60, 1877 (1974).
22. V. K. Vanag and I. R. Epstein, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3231488 131, 104512 (2009).
23. R. J. Field, E. Körös, and R. M. Noyes, J. Am. Chem. Soc. JACSAT 0002-7863 10.1021/ja00780a001 94, 8649 (1972).
24. I. Schreiber and M. Marek, Physica D 0167-2789 10.1016/0167-2789(82) 90021-5 5, 258 (1982).
25. I. Schreiber, M. Holodniok, M. Kubicek, and M. Marek, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01020650 43, 489 (1986).
26. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5109 80, 5109 (1998).
27. V. K. Vanag and I. R. Epstein, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1606677 119, 7297 (2003).
28. J. Carballido-Landeira, PhysChemChemPhys 10, 1094 (2008).
29. A. Kaminaga, V. K. Vanag, and I. R. Epstein, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1888386 122, 174706 (2005). (Pubitemid 40665996)
30. R. McIlwaine, V. K. Vanag, and I. R. Epstein, PhysChemChemPhys 11, 1581 (2009).
31. V. K. Vanag and I. R. Epstein, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.066212 71, 066212 (2005). (Pubitemid 41663856)
32. R. Yoshida, H. Ichijo, T. Hakuta, and T. Yamaguchi, Macrom. Rapid Commun. 1022-1336 10.1002/marc.1995.030160412 16, 305 (1995).
33. V. V. Yashin and A. C. Balazs, Science SCIEAS 0036-8075 10.1126/science.1132412 314, 798 (2006). (Pubitemid 44706642)
34. A. Koseska, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2009.11.007 263, 189 (2010).
35. T. K. Berger, R. Perin, G. Silberberg, and H. Markram, J. Physiol. London 0022-3751 10.1113/jphysiol.2009.176552 587, 5411 (2009).
36. M. S. Baptista and J. Kurths, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.026205 77, 026205 (2008). (Pubitemid 351230761)