Spatially organized dynamical states in chemical oscillator networks: Synchronization, dynamical differentiation, and chimera patterns

PLoS ONE

Volumn 8, Issue 11, 2013, Pages

  Wickramasinghe, Mahesh ^a   Kiss, István Z ^a  

^a Saint Louis University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ELECTROCHEMISTRY; MODELS, CHEMICAL; NEURAL NETWORKS (COMPUTER); NICKEL; OSCILLOMETRY;

EID: 84894048777     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0080586     Document Type: Article

References (46)

1. Epstein IR, Pojman JA (1998) An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos. Oxford: University Press.
2. Kuramoto Y (1984) Chemical Oscillations, Waves and Turbulence. Berlin: Springer Verlag.
3. Winfree AT (1980) The geometry of biological time. New York: Springer-Verlag.
4. Kiss IZ, Hudson JL (2003) Chemical complexity: Spontaneous and engineered structures. AIChE J 49: 2234-2241. doi:10.1002/aic.690490902. (Pubitemid 37163184)
5. Strogatz SH (2001) Exploring complex networks. Nature 410: 268-276. doi:10.1038/35065725. PubMed: 11258382.
6. Newman MEJ (2003) The structure and function of complex networks. Siam Rev 45: 167-256. doi:10.1137/S003614450342480.
7. Albert R, Barabasi AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74: 47-97. doi:10.1103/RevModPhys.74.47.
8. Wiley DA, Strogatz SH, Girvan M (2006) The size of the sync basin. Chaos 16: 015103. doi:10.1063/1.2165594. PubMed: 16599769.
9. Nakao H, Mikhailov AS (2010) Turing patterns in network-organized activator-inhibitor systems. Nat Phys 6: 544-550. doi:10.1038/nphys1651.
10. Arenas A, Díaz-Guilera A, Kurths J, Moreno Y, Zhou C (2008) Synchronization in complex networks. Phys Rep 469: 93-153. doi:10.1016/j. physrep.2008.09.002.
11. Battogtokh D, Kuramoto Y (2002) Coexistence of Coherence and Incoherence. Nonlin Phenom Complex Systems 5: 380-385.
12. Herzog ED (2007) Neurons and networks in daily rhythms. Nat Rev Neurosci 8: 790-802. doi:10.1038/nrn2215. PubMed: 17882255.
13. Buzsáki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304: 1926-1929. doi:10.1126/science.1099745. PubMed: 15218136.
14. Chavez M, Valencia M, Navarro V, Latora V, Martinerie J (2010) Functional Modularity of Background Activities in Normal and Epileptic Brain Networks. Phys Rev Lett 104: 118701. doi:10.1103/PhysRevLett.104.118701. PubMed: 20366507.
15. Dörfler F, Chertkov M, Bullo F (2013) Synchronization in complex oscillator networks and smart grids. Proc Natl Acad Sci USA 110: 2005-2010. doi:10.1073/pnas.1212134110. PubMed: 23319658.
16. Pikovsky AS, Rosenblum M, Kurths J (2001) Synchronization: A Universal Concept in Nonlinear Science. Cambridge: Cambridge University Press.
17. Abrams DM, Strogatz SH (2004) Chimera states for coupled oscillators. Phys Rev Lett 93: 174102. doi:10.1103/PhysRevLett.93.174102. PubMed: 15525081.
18. Wolfrum M, Omel'chenko OE (2011) Chimera states are chaotic transients. Phys Rev E 84: 015201. doi:10.1103/PhysRevE.84.015201. PubMed: 21867244.
19. Hagerstrom AM, Murphy TE, Roy R, Hövel P, Omelchenko I et al. (2012) Experimental observation of chimeras in coupled-map lattices. Nat Phys 8: 658-661. doi:10.1038/nphys2372.
20. Martens EA, Thutupalli S, Fourrière A, Hallatschek O (2013) Chimera states in mechanical oscillator networks. Proc Natl Acad Sci USA 110: 10563-10567. doi:10.1073/pnas.1302880110. PubMed: 23759743.
21. Nevoral V, Votrubova V, Hasal P, Schreiberova L, Marek M (1997) Synchronization of Oscillations and Propagation of Excitations in Circular and Linear Arrays of Coupled CSTRs. J Phys Chem A 101: 4954-4965. doi:10.1021/jp970672k. (Pubitemid 127576535)
22. Votrubova V, Hasal P, Schreiberova L, Marek M (1998) Dynamical Patterns in Arrays of Coupled Chemical Oscillators and Excitators. J Phys Chem A 102: 1318-1328. doi:10.1021/jp973041z. (Pubitemid 128576508)
23. Hauser MJB, Schneider FW (1994) Coupled chaotic states and apparent noise in experiment and model. J Chem Phys 100: 1058-1065. doi:10.1063/1.466637.
24. Hohmann W, Schinor N, Kraus M, Schneider FW (1999) Electrically Coupled Chemical Oscillators and Their Action Potentials. J Phys Chem A 103: 5742-5748. doi:10.1021/jp991224a. (Pubitemid 129579293)
25. Yoshimoto M, Yoshikawa K, Mori Y (1993) Coupling among three chemical oscillators: Synchronization, phase death, and frustration. Phys Rev E 47: 864-874. doi:10.1103/PhysRevE.47.864. PubMed: 9960081.
26. Laplante J-P, Erneux T (1992) Propagation failure and multiple steady states in an array of diffusion coupled flow reactors. Phys A 188: 89-98. doi:10.1016/0378-4371(92)90256-P.
27. Laplante J-P, Erneux T (1992) Propagation failure in arrays of coupled bistable chemical reactors. J Phys Chem 96: 4931-4934. doi:10.1021/j100191a038.
28. Booth V, Erneux T, Laplante J-P (1994) Experimental and Numerical Study of Weakly Coupled Bistable Chemical Reactors. J Phys Chem 98: 6537-6540. doi:10.1021/j100077a019.
29. Taylor AF, Tinsley MR, Wang F, Huang Z, Showalter K (2009) Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators. Science 323: 614-617. doi:10.1126/science.1166253. PubMed: 19179525.
30. Tinsley MR, Nkomo S, Showalter K (2012) Chimera and phase-cluster states in populations of coupled chemical oscillators. Nat Phys 8: 662-665. doi:10.1038/nphys2371.
31. Taylor AF, Tinsley MR, Wang F, Showalter K (2011) Phase clusters in large populations of chemical oscillators. Angew Chem Int Edit 50: 10161-10164. doi:10.1002/anie.201008248. PubMed: 21542070.
32. Toiya M, Vanag VK, Epstein IR (2008) Diffusively coupled chemical oscillators in a microfluidic assembly. Angew Chem Int Edit 47: 7753-7755. doi:10.1002/anie.200802339.
33. Toiya M, Gonzalez-Ochoa HO, Vanag VK, Fraden S, Epstein IR (2010) Synchronization of Chemical Micro-oscillators. J Phys Chem Lett 1: 1241-1246
34. Kiss IZ, Zhai YM, Hudson JL (2002) Emerging coherence in a population of chemical oscillators. Science 296: 1676-1678. doi:10.1126/science.1070757. PubMed: 12040190. (Pubitemid 34579162)
35. Kiss IZ, Zhai YM, Hudson JL (2005) Predicting mutual entrainment of oscillators with experiment-based phase models. Phys Rev Lett 94: 248301. doi:10.1103/PhysRevLett.94.248301. PubMed: 16090583.
36. Wang W, Kiss IZ, Hudson JL (2000) Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. Chaos 10: 248-256. doi:10.1063/1.166470. PubMed: 12779380.
37. Wu CW, Chua LO (1996) On a conjecture regarding the synchronization in an array of linearly coupled dynamical systems. IEEE Trans Circuits Syst I-Fundam Theor Appl 43: 161-165. (Pubitemid 126776655)
38. Manrubia SC, Mikhailov AS (1999) Mutual synchronization and clustering in randomly coupled chaotic dynamical networks. Phys Rev E 60: 1579-1589. doi:10.1103/PhysRevE.60.1579. PubMed: 11969920. (Pubitemid 129691327)
39. Kiss IZ, Rusin CG, Kori H, Hudson JL (2007) Engineering complex dynamical structures: Sequential patterns and desynchronization. Science 316: 1886-1889. doi:10.1126/science.1140858. PubMed: 17525302. (Pubitemid 47025785)
40. Hansel D, Mato G, Meunier C (1993) Clustering and slow switching in globally coupled phase oscillators. Phys Rev E 48: 3470-3477. doi:10.1103/PhysRevA.48.3470. PubMed: 9961005.
41. Nicosia V, Valencia M, Chavez M, Díaz-Guilera A, Latora V (2013) Remote Synchronization Reveals Network Symmetries and Functional Modules. Phys Rev Lett 110: 174102. doi:10.1103/PhysRevLett.110.174102. PubMed: 23679731.
42. Kaneko K (1990) Clustering, Coding, Switching, Hierarchical Ordering, and Control in a Network of Chaotic Elements. Phys D 41: 137-172. doi:10.1016/0167-2789(90)90119-A.
43. Wang W, Kiss IZ, Hudson JL (2001) Clustering of arrays of chaotic chemical oscillators by feedback and forcing. Phys Rev Lett 86: 4954-4957. doi:10.1103/PhysRevLett.86.4954. PubMed: 11384390. (Pubitemid 32505542)
44. Pecora LM (1998) Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems. Phys Rev E 58: 347-360. doi:10.1103/PhysRevE.58.347.
45. Kiss IZ, Wang W, Hudson JL (2000) Complexity of globally coupled chaotic electrochemical oscillators. Phys Chem Chem Phys 2: 3847-3854. doi:10.1039/b003812l.
46. Jia Y, Kiss IZ (2012) Spontaneously synchronized electrochemical micro-oscillators with nickel electrodissolution. J Phys Chem C 116: 19290-19299. doi:10.1021/jp3047278.