Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection

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

Volumn 89, Issue 5, 2014, Pages

  Siebert, Julien ^a   Alonso, Sergio ^b   Bär, Markus ^b   Schöll, Eckehard ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; DYNAMIC MODELS; LINEAR EQUATIONS; NUMERICAL METHODS;

BISTABLE REACTION-DIFFUSION SYSTEM; COMPLEX PATTERN; NONLOCAL COUPLING; NUMERICAL INTEGRATIONS; REACTION DIFFUSION; REACTION DIFFUSION EQUATIONS; REACTION-DIFFUSION MODELS; SPATIALLY HOMOGENEOUS;

DIFFUSION IN LIQUIDS;

CHEMICAL MODEL; COMPUTER SIMULATION; DIFFUSION; FLOW KINETICS; NONLINEAR SYSTEM; OSCILLOMETRY; PROCEDURES;

COMPUTER SIMULATION; DIFFUSION; MODELS, CHEMICAL; NONLINEAR DYNAMICS; OSCILLOMETRY; RHEOLOGY;

EID: 84901297582     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.89.052909     Document Type: Article

References (73)

1. H. Haken, Synergetics, An Introduction, 3rd ed. (Springer, Berlin, 1983).
2. A. S. Mikhailov, Foundations of Synergetics, 2nd ed. (Springer, Berlin, 1994), Vol. I.
3. Chemical Waves and Patterns, edited by R. Kapral and K. Showalter (Kluwer, Dordrecht, 1995).
4. J. P. Keener and J. Sneyd, Mathematical Physiology (Springer, New York, 1998).
5. S. Kondo and T. Miura, Science 329, 1616 (2010). SCIEAS 0036-8075 10.1126/science.1179047
6. A. T. Winfree, When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias (Princeton University Press, Princeton, NJ, 1987); includes indexes.
7. J. M. Davidenko, A. M. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature (London) 355, 349 (1992). NATUAS 0028-0836 10.1038/355349a0
8. N. A. Gorelova and J. Bures, J. Neurobiol. 14, 353 (1983). JNEUBZ 0022-3034 10.1002/neu.480140503
9. M. A. Dahlem and S. C. Müller, Exp. Brain Res. 115, 319 (1997). EXBRAP 0014-4819 10.1007/PL00005700 (Pubitemid 27261147)
10. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin, 1984).
11. M. Falcke and H. Engel, Phys. Rev. E 50, 1353 (1994). 1063-651X 10.1103/PhysRevE.50.1353
12. M. Bär, M. Falcke, M. Hildebrand, M. Neufeld, H. Engel, and M. Eiswirth, Int. J. Bifurcation Chaos Appl. Sci. Eng. 4, 499 (1994).
13. M. Falcke, H. Engel, and M. Neufeld, Phys. Rev. E 52, 763 (1995). 1063-651X 10.1103/PhysRevE.52.763
14. M. Bertram, C. Beta, M. Pollmann, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Phys. Rev. E 67, 036208 (2003). 1063-651X 10.1103/PhysRevE.67.036208
15. C. Beta, M. Bertram, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Phys. Rev. E 67, 046224 (2003). 1063-651X 10.1103/PhysRevE.67.046224
16. C. Beta, M. G. Moula, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Phys. Rev. Lett. 93, 188302 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93. 188302
17. U. Middya, M. Sheintuch, M. D. Graham, and D. Luss, Physica D 63, 393 (1992). 10.1016/0167-2789(93)90119-L
18. M. Sheintuch and S. Shvartsman, AIChE J. 42, 1041 (1996). AICEAC 0001-1541 10.1002/aic.690420416
19. F. Plenge, P. Rodin, E. Schöll, and K. Krischer, Phys. Rev. E 64, 056229 (2001). 1063-651X 10.1103/PhysRevE.64.056229
20. M. Meixner, P. Rodin, E. Schöll, and A. Wacker, Eur. Phys. J. B 13, 157 (2000). EPJBFY 1434-6028 10.1007/s100510050019
21. E. Schöll, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors, Nonlinear Science Series Vol. 10 (Cambridge University Press, Cambridge, 2001).
22. A. S. Mikhailov and K. Showalter, Phys. Rep. 425, 79 (2006). PRPLCM 0370-1573 10.1016/j.physrep.2005.11.003 (Pubitemid 43174943)
23. M. Sheintuch, Physica D 102, 125 (1996). 10.1016/S0167-2789(96)00219-9
24. A. Yochelis and M. Sheintuch, Phys. Rev. E 80, 056201 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.80.056201
25. A. Yochelis and M. Sheintuch, Phys. Chem. Chem. Phys. 11, 9210 (2009). PPCPFQ 1463-9076 10.1039/b903266e
26. A. Yochelis and M. Sheintuch, Phys. Chem. Chem. Phys. 12, 3957 (2010). PPCPFQ 1463-9076 10.1039/b921918h
27. A. Yochelis and M. Sheintuch, Phys. Rev. E 81, 025203 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.81.025203
28. A. B. Rovinsky and M. Menzinger, Phys. Rev. Lett. 69, 1193 (1992). PRLTAO 0031-9007 10.1103/PhysRevLett.69.1193
29. A. B. Rovinsky and M. Menzinger, Phys. Rev. Lett. 70, 778 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.70.778
30. Y. Khazan and L. M. Pismen, Phys. Rev. Lett. 75, 4318 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett.75.4318
31. Y. Balinsky (Khazan) and L. M. Pismen, Phys. Rev. E 58, 4524 (1998). 1063-651X 10.1103/PhysRevE.58.4524
32. R. A. Satnoianu, J. H. Merkin, and S. K. Scott, Physica D 124, 345 (1998). PDNPDT 0167-2789 10.1016/S0167-2789(98)00206-1
33. A. Tóth, D. Horváth, and W. van Saarloos, J. Chem. Phys. 111, 10964 (1999). JCPSA6 0021-9606 10.1063/1.480459
34. H. Malchow, J. Marine Syst. 7, 193 (1996). JMASE5 0924-7963 10.1016/0924-7963(95)00012-7
35. C. A. Klausmeier, Science 284, 1826 (1999). SCIEAS 0036-8075 10.1126/science.284.5421.1826 (Pubitemid 29291430)
36. J. von Hardenberg, E. Meron, M. Shachak, and Y. Zarmi, Phys. Rev. Lett. 87, 198101 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.87.198101
37. F. Borgogno, P. D'Odorico, F. Laio, and L. Ridolfi, Rev. Geophys. 47, 1 (2009). REGEEP 8755-1209 10.1029/2007RG000256
38. D. M. Petrich and R. E. Goldstein, Phys. Rev. Lett. 72, 1120 (1994). PRLTAO 0031-9007 10.1103/PhysRevLett.72.1120
39. L. M. Pismen, Patterns and Interfaces in Dissipative Dynamics, Springer Series in Synergetics (Springer, Berlin, 2006).
40. E. M. Nicola, M. Or-Guil, W. Wolf, and M. Bär, Phys. Rev. E 65, 055101 (R) (2002). 1063-651X 10.1103/PhysRevE.65.055101 (Pubitemid 40606824)
41. D. Tanaka and Y. Kuramoto, Phys. Rev. E 68, 026219 (2003). 1063-651X 10.1103/PhysRevE.68.026219
42. S.-i. Shima and Y. Kuramoto, Phys. Rev. E 69, 036213 (2004). PLEEE8 1539-3755 10.1103/PhysRevE.69.036213
43. A. Das and C. D. Gilbert, Nature (London) 399, 655 (1999). NATUAS 0028-0836 10.1038/21371 (Pubitemid 29289053)
44. K. Kang, M. Shelley, and H. Sompolinsky, Proc. Natl. Acad. Sci. U.S.A. 100, 2848 (2003). PNASA6 0027-8424 10.1073/pnas.0138051100 (Pubitemid 36297587)
45. X. Xu, W. Bosking, G. Sáry, J. Stefansic, D. Shima, and V. Casagrande, J. Neurosci. 24, 6237 (2004). JNRSDS 0270-6474 10.1523/JNEUROSCI. 1144-04.2004 (Pubitemid 38944213)
46. J. Christoph and M. Eiswirth, Chaos 12, 215 (2002). CHAOEH 1054-1500 10.1063/1.1449956
47. M. Sheintuch and O. Nekhamkina, J. Chem. Phys. 107, 8165 (1997). JCPSA6 0021-9606 10.1063/1.3427649
48. G. Bordyugov and H. Engel, Phys. Rev. E 74, 016205 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.74.016205 (Pubitemid 44091269)
49. P. Colet, M. A. Matias, L. Gelens, and D. Gomila, Phys. Rev. E 89, 012914 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.012914
50. L. Gelens, M. A. Matias, D. Gomila, T. Dorissen, and P. Colet, Phys. Rev. E 89, 012915 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.012915
51. N. Mazouz, G. Flätgen, and K. Krischer, Phys. Rev. E 55, 2260 (1997). 1063-651X 10.1103/PhysRevE.55.2260
52. M. Hildebrand, H. Skødt, and K. Showalter, Phys. Rev. Lett. 87, 088303 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.87.088303
53. E. M. Nicola, M. Bär, and H. Engel, Phys. Rev. E 73, 066225 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.73.066225 (Pubitemid 43980051)
54. R. Friedrichs and A. Engel, Europhys. Lett. 63, 826 (2003). EULEEJ 0295-5075 10.1209/epl/i2003-00605-7 (Pubitemid 37180507)
55. J. Christoph, R. D. Otterstedt, M. Eiswirth, N. I. Jaeger, and J. L. Hudson, J. Chem. Phys. 110, 8614 (1999). JCPSA6 0021-9606 10.1063/1.478768
56. Y. J. Li, J. Oslonovitch, N. Mazouz, F. Plenge, K. Krischer, and G. Ertl, Science 291, 2395 (2001). SCIEAS 0036-8075 10.1126/science.1057830 (Pubitemid 32231798)
57. H. Varela, C. Beta, A. Bonnefont, and K. Krischer, Phys. Rev. Lett. 94, 174104 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.174104 (Pubitemid 41492262)
58. B. Belintsev, M. Livshits, and M. Volkenstein, Z. Phys. B 44, 345 (1981). ZPBBDJ 0340-224X 10.1007/BF01294173
59. M. A. Dahlem, F. M. Schneider, and E. Schöll, Chaos 18, 026110 (2008). CHAOEH 1054-1500 10.1063/1.2937120
60. F. M. Schneider, E. Schöll, and M. A. Dahlem, Chaos 19, 015110 (2009). CHAOEH 1054-1500 10.1063/1.3096411
61. M. A. Dahlem, R. Graf, A. J. Strong, J. P. Dreier, Y. A. Dahlem, M. Sieber, W. Hanke, K. Podoll, and E. Schöll, Physica D 239, 889 (2010). PDNPDT 0167-2789 10.1016/j.physd.2009.08.009
62. Y. Kuramoto and D. Battogtokh, Nonlinear Phenom. Complex Syst. (Minsk, Belarus) 5, 380 (2002).
63. D. M. Abrams and S. H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.174102
64. A. Hagerstrom, T. E. Murphy, R. Roy, P. Hövel, I. Omelchenko, and E. Schöll, Nat. Phys. 8, 658 (2012). 1745-2473 10.1038/nphys2372
65. M. R. Tinsley, S. Nkomo, and K. Showalter, Nat. Phys. 8, 662 (2012). 1745-2473 10.1038/nphys2371
66. E. A. Martens, S. Thutupalli, A. Fourrière, and O. Hallatschek, Proc. Natl. Acad. Sci. U.S.A. 110, 10563 (2013). PNASA6 0027-8424 10.1073/pnas.1302880110
67. I. Omelchenko, O. E. Omel'chenko, P. Hövel, and E. Schöll, Phys. Rev. Lett. 110, 224101 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110. 224101
68. M. Kim, M. Bertram, M. Pollmann, A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, Science 292, 1357 (2001). SCIEAS 0036-8075 10.1126/science.1059478 (Pubitemid 32476218)
69. Y. N. Kyrychko, K. B. Blyuss, S. J. Hogan, and E. Schöll, Chaos 19, 043126 (2009). CHAOEH 1054-1500 10.1063/1.3270048
70. H. Malchow and L. Schimansky-Geier, Noise and Diffusion in Bistable Nonequilibrium Systems (B. G. Teubner, Berlin, 1985).
71. F. Schlögl, Z. Phys. 253, 147 (1972). EPJAFV 1434-6001 10.1007/BF01379769
72. F. Schlögl, C. Escher, and R. S. Berry, Phys. Rev. A 27, 2698 (1983). 0556-2791 10.1103/PhysRevA.27.2698
73. Note that the Fourier transform of the function (Equation presented) is (Equation presented).