Reaction-Cattaneo systems with fluctuating relaxation time

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

Volumn 81, Issue 2, 2010, Pages

  Ghosh, Pushpita ^a   Sen, Shrabani ^a   Ray, Deb Shankar ^a  

^a DEPARTMENT OF MATERIALS SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSIVE FLUX; DOUBLE HOPF BIFURCATION; OSCILLATORY SOLUTIONS; SPATIOTEMPORAL PATTERNS;

DYNAMICAL SYSTEMS; HOPF BIFURCATION; NONLINEAR SYSTEMS;

RELAXATION PROCESSES;

EID: 77249124419     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.026205     Document Type: Article

References (42)

1. I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics; Oscillations, Waves, Patterns and Chaos (Oxford University Press, New York, 1998).
2. P. Gray and S. K. Scott, Chemical Oscillations and Instabilities (Clarendon, Oxford, 1990).
3. H. Meinhardt, Models of Biological Pattern formation (Academic, London, 1982).
4. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993). 10.1103/RevModPhys.65.851
5. R. Furth, Z. Phys. 2, 244 (1920). 10.1007/BF01328731
6. G. I. Taylor, Proc. London Math. Soc. s2, 196 (1921). 10.1112/plms/s2-20.1.196
7. G. W. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
8. W. Horsthemke, Phys. Rev. E 60, 2651 (1999). 10.1103/PhysRevE.60.2651
9. C. Cattaneo, C. R. Acad. Sci., Paris 247, 431 (1958)
10. D. D. Joseph and L. Preziosi, Rev. Mod. Phys. 61, 41 (1989). 10.1103/RevModPhys.61.41
11. P. Ghosh, S. Sen, and D. S. Ray, Phys. Rev. E 79, 016206 (2009) 10.1103/PhysRevE.79.016206
12. S. Kar, S. K. Banik, and D. S. Ray, J. Phys. A 36, 2771 (2003). 10.1088/0305-4470/36/11/308
13. Th. Gallay and G. Raugel, Z. Angew. Math. Phys. 48, 451 (1997). 10.1007/s000330050043
14. Th. Gallay and G. Raugel, J. Differ. Equations 150, 42 (1998). 10.1006/jdeq.1998.3459
15. Th. Gallay and G. Raugel, e-print arXiv:patt-sol/9809007.
16. X. Cai, J. Chem. Phys. 126, 124108 (2007). 10.1063/1.2710253
17. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Physica D 129, 15 (1999). 10.1016/S0167-2789(99)00004-4
18. E. I. Volkov and D. V. Volkov, Phys. Rev. E 65, 046232 (2002). 10.1103/PhysRevE.65.046232
19. S. H. Park, S. Kim, H. B. Pyo, and S. Lee, Phys. Rev. E 60, 4962 (1999). 10.1103/PhysRevE.60.4962
20. R. Herrero, M. Figueras, J. Rius, F. Pi, and G. Orriols, Phys. Rev. Lett. 84, 5312 (2000). 10.1103/PhysRevLett.84.5312
21. A. Takamatsu, T. Fujii, and I. Endo, Phys. Rev. Lett. 85, 2026 (2000). 10.1103/PhysRevLett.85.2026
22. F. R. Sharpe and A. J. Lotka, Am. J. Trop. Med. Hyg. 3, 96 (1923).
23. K. W. Smith and R. M. Noyes, J. Phys. Chem. 87, 1520 (1983). 10.1021/j100232a014
24. E. C. Zimmermann, M. Schell, and J. Ross, J. Chem. Phys. 81, 1327 (1984). 10.1063/1.447764
25. A. G. Balanov, N. B. Janson, and E. Scholl, Phys. Rev. E 71, 016222 (2005). 10.1103/PhysRevE.71.016222
26. M. R. Roussel, J. Phys. Chem. 100, 8323 (1996). 10.1021/jp9600672
27. I. R. Epstein, J. Chem. Phys. 92, 1702 (1990). 10.1063/1.458052
28. I. R. Epstein and Y. Luo, J. Chem. Phys. 95, 244 (1991). 10.1063/1.461481
29. F. Ghiringhelli and M. N. Zervas, Phys. Rev. E 65, 036604 (2002). 10.1103/PhysRevE.65.036604
30. F. M. Atay, Phys. Rev. Lett. 91, 094101 (2003). 10.1103/PhysRevLett.91. 094101
31. L. Ji and Q. S. Li, J. Chem. Phys. 123, 094509 (2005). 10.1063/1.2041427
32. J. Unkelbach, A. Amann, W. Just, and E. Scholl, Phys. Rev. E 68, 026204 (2003). 10.1103/PhysRevE.68.026204
33. J. Pomplun, A. Amann, and E. Scholl, Europhys. Lett. 71, 366 (2005). 10.1209/epl/i2005-10100-9
34. G. Stegemann, A. G. Balanov, and E. Scholl, Phys. Rev. E 73, 016203 (2006). 10.1103/PhysRevE.73.016203
35. E. A. Novikov, Sov. Phys. JETP 20, 1290 (1965)
36. See for its use S. S. Riaz, S. Dutta, and D. S. Ray, Phys. Rev. E 71, 036216 (2005) 10.1103/PhysRevE.71.036216
37. S. S. Riaz, S. Dutta, S. Kar, and D. S. Ray, Eur. Phys. J. B 47, 255 (2005). 10.1140/epjb/e2005-00314-1
38. J. Garca-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer-Verlag, New York, 1999).
39. P. De Kepper, J. Boissonade, and I. R. Epstein, J. Phys. Chem. 94, 6525 (1990). 10.1021/j100380a004
40. V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Phys. Rev. Lett. 64, 2953 (1990). 10.1103/PhysRevLett.64.2953
41. A. Hanna, A. Saul, and K. Showalter, J. Am. Chem. Soc. 104, 3838 (1982). 10.1021/ja00378a011
42. D. Horvath and K. Showalter, J. Chem. Phys. 102, 2471 (1995). 10.1063/1.468676