Kinetic equations for reaction-subdiffusion systems: Derivation and stability analysis

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

Volumn 74, Issue 6, 2006, Pages

  Yadav, A ^a   Horsthemke, Werner ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY (SPECIFIC GRAVITY); MARKOV PROCESSES; REACTION KINETICS; SHAPE MEMORY EFFECT; TRANSPORT PROPERTIES;

KINETIC EQUATIONS; SUBDIFFUSIVE SYSTEMS; TURING INSTABILITY; TURING THRESHOLD;

DIFFUSION;

EID: 33846399755     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.066118     Document Type: Article

References (48)

1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (John Wiley and Sons, New York, 1977).
2. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.65.851 65, 851 (1993).
3. D. Walgraef, Spatio-Temporal Pattern Formation (Springer-Verlag, Berlin, 1996).
4. R. N. Ghosh and W. W. Webb, Biophys. J. BIOJAU 0006-3495 68, 766 (1994).
5. M. J. Saxton, Biophys. J. BIOJAU 0006-3495 66, 394 (1994).
6. M. J. Saxton, Biophys. J. BIOJAU 0006-3495 70, 1250 (1996).
7. B. Berkowitz, J. Klafter, R. Metzler, and H. Scher, Water Resour. Res. WRERAQ 0043-1397 10.1029/2001WR001030 38, 1191 (2002).
8. E. W. Montroll and M. F. Shlesinger, in Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, edited by, J. L. Lebowitz, and, E. W. Montroll, (Elsevier Science Publishers, Amsterdam, 1984), p. 1.
9. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
10. A. Compte, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.4191 53, 4191 (1996).
11. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.3081 35, 3081 (1987).
12. R. Metzler and J. Klafter, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/31/R01 37, R161 (2004).
13. H. Scher and E. W. Montroll, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.12.2455 12, 2455 (1975).
14. D. ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, U.K., 2000).
15. B. I. Henry and S. L. Wearne, Physica A PHYADX 0378-4371 10.1016/S0378-4371(99)00469-0 276, 448 (2000).
16. B. I. Henry and S. L. Wearne, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139900375227 62, 870 (2002).
17. B. I. Henry, T. A. M. Langlands, and S. L. Wearne, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.026101 72, 026101 (2005).
18. K. Seki, M. Wojcik, and M. Tachiya, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1605946 119, 7525 (2003).
19. G. Hornung, B. Berkowitz, and N. Barkai, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.041916 72, 041916 (2006).
20. M. O. Vlad and J. Ross, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.061908 66, 061908 (2002).
21. M. O. Vlad, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/20/11/039 20, 3367 (1987).
22. S. B. Yuste and K. Lindenberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.118301 87, 118301 (2001).
23. S. B. Yuste and K. Lindenberg, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(02)00546-3 284, 169 (2002).
24. S. B. Yuste, L. Acedo, and K. Lindenberg, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.036126 69, 036126 (2004).
25. J. Y. Sung, E. Barkai, R. J. Sibley, and S. Lee, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1448294 116, 2338 (2002).
26. J. Sung and R. J. Silbey, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.160601 91, 160601 (2003).
27. K. Seki, M. Wojcik, and M. Tachiya, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1587126 119, 2165 (2003).
28. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B PTRBAE 0962-8436 327, 37 (1952).
29. E. Scalas, R. Gorenflo, and F. Mainardi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.011107 69, 011107 (2004).
30. I. M. Sokolov, M. G. W. Schmidt, and F. Sagués, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.031102 73, 031102 (2006).
31. M. G. W. Schmidt, F. Sagués, and I. M. Sokolov, e-print cond-mat/0608117.
32. Wilbur R. LePage, Complex Variables and the Laplace Transform for Engineers (Dover Publications, New York, 1980).
33. J. D. Murray, Asymptotic Analysis (Springer-Verlag, New York, 1984).
34. R. Kapral and K. Showalter, Chemical Waves and Patterns (Kluwer, Dordrecht, 1995).
35. J. D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications (Springer, New York, 2003).
36. L. A. Segel, Modeling Dynamic Phenomena in Molecular and Cellular Biology (Cambridge University Press, Cambridge, U.K., 1984).
37. J. Schnakenberg, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(79) 90042-0 81, 389 (1979).
38. A. Yadav and W. Horsthemke (unpublished).
39. M. Weiss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.036213 68, 036213 (2003).
40. S. Fedotov and Y. Okuda, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.021113 66, 021113 (2002).
41. L. You and J. Yin, J. Theor. Biol. JTBIAP 0022-5193 10.1006/jtbi.1999. 1001 200, 365 (1999).
42. J. Fort and V. Méndez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.178101 89, 178101 (2002).
43. J. Fort, J. Pérez, E. Ubeda, and F. J. García, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.021907 73, 021907 (2006).
44. V. Ortega-Cejas, J. Fort, and V. Méndez, Ecology ECOLAR 0012-9658 85, 258 (2004).
45. J. Fort and V. Méndez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.867 82, 867 (1999).
46. J. Fort, D. Jana, and J. Humet, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.031913 70, 031913 (2004).
47. J. Fort, T. Pujol, and L. L. Cavalli-Sforza, Cambridge Archaeol. J. 14, 53 (2004).
48. T. Kosztołowicz, K. Dworecki, and S. Mrówczyński, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.041105 71, 041105 (2005).