Nonlinear dynamics of finite perturbation: Collapse and revival of spatial patterns

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

Volumn 79, Issue 1, 2009, 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

LINEAR STABILITY ANALYSIS; NONLINEAR ANALYSIS; STABILITY; SYSTEM STABILITY;

COLLAPSE AND REVIVALS; CUBIC POLYNOMIALS; FICK'S LAW OF DIFFUSIONS; LIMIT CYCLES; LINEAR STABILITIES; MACROSCOPIC LEVELS; NON-LINEAR DYNAMICS; NON-LINEAR STABILITY ANALYSIS; REACTION TIME; REACTION-DIFFUSION SYSTEMS; SOURCE TERMS; SPATIAL PATTERNS; SPATIO-TEMPORAL INSTABILITIES; STEADY STATE; TIME PERIODS; UNDERLYING DYNAMICS;

DYNAMICS;

EID: 60149108527     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.016206     Document Type: Article

References (40)

1. See, for example, S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, MA, 1994).
2. J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, NewYork, 1999).
3. N. F. Britton, Reaction-diffusion Equations and Their Application to Biology (Academic, New York, 1986).
4. A. Okubo, Diffusion and Ecological Problems (Spinger, Berlin, 1980).
5. I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns and Chaos (Oxford University Press, New York, 1998).
6. P. Gray and S. K. Scott, Chemical Oscillations and Instabilities (Clarendon Press, Oxford, 1990).
7. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952). 10.1098/rstb.1952.0012
8. P. De Kepper, J. Boissonade, and I. R. Epstein, J. Phys. Chem. 94, 6525 (1990). 10.1021/j100380a004
9. Oscillations and Travelling Waves in Chemical Systems, edited by, R. J. Feld, and, M. Burger, (Wiley, NewYork, 1985).
10. H. Meinhardt, Models of Biological Pattern Formation (Academic, London, 1982).
11. A. Becker and L. Kramer, Phys. Rev. Lett. 73, 955 (1994). 10.1103/PhysRevLett.73.955
12. C. Van den Broeck, J. M. R. Parrondo, J. Armero, and A. Hernandez-Machado, Phys. Rev. E 49, 2639 (1994). 10.1103/PhysRevE.49.2639
13. P. S. Landa, A. A. Zaikin, and L. Schimansky-Geier, Chaos, Solitons Fractals 9, 1367 (1998). 10.1016/S0960-0779(98)00069-1
14. S. Dutta, S. S. Riaz and D. S. Ray, Phys. Rev. E 71, 036216 (2005). 10.1103/PhysRevE.71.036216
15. S. S. Riaz, S. Dutta, S. Kar, and D. S. Ray, Eur. Phys. J. B 47, 255 (2005). 10.1140/epjb/e2005-00314-1
16. S. S. Riaz, R. Sharma, S. P. Bhattacharyya, and D. S. Ray, J. Chem. Phys. 127, 064503 (2007). 10.1063/1.2759212
17. U. Dressler and J. D. Farmer, Physica D 59, 365 (1992). 10.1016/0167-2789(92)90076-Y
18. E. Aurell, B. Boffetta, A. Crisanti, G. Paladin, and A. Valpiani, Phys. Rev. Lett. 77, 1262 (1996). 10.1103/PhysRevLett.77.1262
19. A. Torcini, P. Grassberger, and A. Politi, J. Phys. A 28, 4533 (1995). 10.1088/0305-4470/28/16/011
20. M. Cencini and A. Torcini, Phys. Rev. E 63, 056201 (2001). 10.1103/PhysRevE.63.056201
21. C. Cattaneo, C. R. Acad. Sci. URSS 247, 431 (1958).
22. K. P. Hadeler, in Reaction Transport Systems in Mathematics Inspired by Biology, edited by, V. Capasso, and, O. Dickmann, (Springer-Verlag, Berlin, 1998).
23. T. Hillen, Math. Methods Appl. Sci. 8, 507 (1998). 10.1142/ S0218202598000238
24. W. Horsthemke, Phys. Rev. E 60, 2651 (1999). 10.1103/PhysRevE.60.2651
25. S. Kar, S. K. Banik, and D. S. Ray, Phys. Rev. E 65, 061909 (2002). 10.1103/PhysRevE.65.061909
26. S. Kar, S. K. Banik, and D. S. Ray, J. Phys. A 36, 2771 (2003). 10.1088/0305-4470/36/11/308
27. Th. Gallay and G. Raugel, ZAMP 48, 451 (1997); 10.1007/s000330050043
28. Th. Gallay and G. Raugel, J. Differ. Equations 150, 42 (1998). 10.1006/jdeq.1998.3459
29. K. P. Hadeler, Cad. Appl. Math. Qu. 2, 27 (1994).
30. V. Mendez and A. Compte, Physica A 260, 90 (1998). 10.1016/S0378-4371(98) 00281-7
31. K. K. Manne, A. J. Hurd, and V. M. Kenkre, Phys. Rev. E 61, 4177 (2000); 10.1103/PhysRevE.61.4177
32. S. Fedotov, Phys. Rev. Lett. 86, 926 (2001); 10.1103/PhysRevLett.86.926
33. J. M. Sancho and A. Sanchez, Phys. Rev. E 63, 056608 (2001). 10.1103/PhysRevE.63.056608
34. Ya. B. Zeldovich and D. A. Frank-Kamenetsky, Dokl. Akad. Nauk SSSR 19, 693 (1938);
35. Ya. B. Zeldovich and G. I. Darrenblalt, Combust. Flame 3, 61 (1959). 10.1016/0010-2180(59)90007-0
36. F. Offner, A. Weinberg, and C. Young, Bull. Math. Biophys. 2, 89 (1940). 10.1007/BF02478173
37. P. de Kepper, I. R. Epstein, and K. Kautin, J. Am. Chem. Soc. 103, 6121 (1981). 10.1021/ja00410a023
38. S. Dutta and D. S. Ray, Phys. Rev. E 75, 066206 (2007); 10.1103/PhysRevE.75.066206
39. S. Dutta and D. S. Ray, Phys. Rev. E 77, 036202 (2008). 10.1103/PhysRevE.77.036202
40. J. K. Bhattacharjee, A. K. Mallik, and S. Chakraborty, Indian J. Phys., A 81, 11 (2007).