Global analysis of pattern selection and bifurcations in monostable reaction-diffusion systems

Physica A: Statistical Mechanics and its Applications

Volumn 237, Issue 1-2, 1997, Pages 135-149

  Izus G ^a   Deza, R ^a   Borzi, C ^b   Wio, H S ^c  

^a UNIVERSIDAD NACIONAL DE MAR DEL PLATA   (Argentina)

^b MONDITEC SA   (Argentina)

^c INSTITUTO BALSEIRO   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; DIFFUSION; MATHEMATICAL MODELS; PIECEWISE LINEAR TECHNIQUES;

GLOBAL ANALYSIS; MONOSTABLE REACTION DIFFUSION SYSTEM; PATTERN SELECTION;

MOLECULAR DYNAMICS;

EID: 0031098829     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(96)00382-2     Document Type: Article

References (52)

1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley. New York, 1976).
2. H. Haken, Synergetics: An introduction, 2nd Ed. (Springer, New York, 1978).
3. M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65 (1993) 851.
4. C. Vidal and A. Pacault, eds., Non-Equilibrium Dynamics in Chemical Systems, (Springer, Berlin, 1984).
5. P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems (Springer, Berlin, 1979); P.C. Fife, Current topics in reaction-diffusion systems, in: Nonequilibrium Cooperative Phenomena in Physics and Related Fields, ed. M.G. Velarde (Plenum Press, New York, 1984) p. 371.
6. P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems (Springer, Berlin, 1979); P.C. Fife, Current topics in reaction-diffusion systems, in: Nonequilibrium Cooperative Phenomena in Physics and Related Fields, ed. M.G. Velarde (Plenum Press, New York, 1984) p. 371.
7. G. Nicolis, T. Erneux and M. Herschkowitz-Kaufman, Pattern formation in reacting and diffusing systems, in: Advances in Chemical Physics, Vol.38, eds. I. Prigogine and S. Rice (Wiley, New York, 1978).
8. J.D. Murray, Mathematical Biology (Springer, Berlin, 1985); J.D. Murray, Nonlinear Differential Equation Models in Biology (Clarendon Press, Oxford, 1977).
9. J.D. Murray, Mathematical Biology (Springer, Berlin, 1985); J.D. Murray, Nonlinear Differential Equation Models in Biology (Clarendon Press, Oxford, 1977).
10. F.C. Hoppensteadt, Mathematical Methods in Population Biology (Cambridge University Press, Cambridge, 1982).
11. H.S. Wio, An Introduction to Stochastic Processes and Nonequilibrium Statistical Physics (World Scientific, Singapore, 1994).
12. D. Bedeaux, P. Mazur and R.A. Pasmanter, Physica A 86 (1977) 355; D. Bedeaux and P. Mazur, Physica A 105 (1981) 1.
13. D. Bedeaux, P. Mazur and R.A. Pasmanter, Physica A 86 (1977) 355; D. Bedeaux and P. Mazur, Physica A 105 (1981) 1.
14. A.S. Mikhailov, Foundations of Synergetics I (Springer, Berlin, 1990).
15. C. Borzi, H.L. Frisch, R. Gianotti and J.K. Percus, J. Phys. A 23 (1990) 4823.
16. S.A. Hassan, D.H. Zanette and H.S. Wio, J. Phys. A 27 (1994) 5129.
17. C. Borzi and H.S. Wio, Phys. Lett.A 160 (1991) 247.
18. C.L. Schat and H.S. Wio, Physica A 180 (1992) 295.
19. H. Wio, G. Izús, O. Ramírez, R. Deza and C. Borzi, J. Phys. A 26 (1993) 4281.
20. G. Izús, R. Deza, O. Ramírez, H. Wio, D. Zanette and C. Borzi, Phys. Rev. E 52 (1995) 129.
21. D. Zanette, H. Wio and R. Deza, Phys. Rev. E 53 (1996) 353.
22. G. Izús, H. Wio, J. Reyes de Rueda, O. Ramírez and R. Deza. Int. J. Mod. Phys. B 10 (11) (1996) 1273.
23. V. Castets, E. Dulos, J. Boissonade and P. de Keeper, Phys. Rev. Lett. 64 (1990) 2953.
24. S.P. Fedotov, Phys. Lett. A 176 (1993) 220.
25. M Kerszberg, Phys. Rev. A 28 (1983) 1198; M. de la Torre and I. Rehberg, Phys. Rev. A 42 (1990) 2096; ibid. 42 (1990) 5998.
26. M Kerszberg, Phys. Rev. A 28 (1983) 1198; M. de la Torre and I. Rehberg, Phys. Rev. A 42 (1990) 2096; ibid. 42 (1990) 5998.
27. M Kerszberg, Phys. Rev. A 28 (1983) 1198; M. de la Torre and I. Rehberg, Phys. Rev. A 42 (1990) 2096; ibid. 42 (1990) 5998.
28. G. Izús, O. Ramírez, R. Deza and H. Wio, J. Chem. Phys., in press.
29. J. Viñals, E. Hernandez-García, M. San Miguel and R. Toral; Phys. Rev. Lett. 70, 3576 (1993); E. Hernandez-García, J. Viñals, R. Toral and M. San Miguel, Phys. Rev. Lett. 70 (1993) 3576.
30. J. Viñals, E. Hernandez-García, M. San Miguel and R. Toral; Phys. Rev. Lett. 70, 3576 (1993); E. Hernandez-García, J. Viñals, R. Toral and M. San Miguel, Phys. Rev. Lett. 70 (1993) 3576.
31. J. Keizer, Statistical Thermodynamics of Nonequilibrium Processes (Springer, New York, 1987).
32. R.A. Fisher, Ann. Eugen. 7 (1936) 355-369.
33. J. Canosa, J. Math. Phys. 10 (1969) 1862.
34. W. van Saarlos, Phys. Rev. A 37 (1988) 211; 39 (1989) 6367.
35. W. van Saarlos, Phys. Rev. A 37 (1988) 211; 39 (1989) 6367.
36. A. Kolmogorov, I. Petrovskii and N. Piscunov, Moscow Univ. Bull. Math. 1 (1937) 1-25.
37. D.G. Aronson, E.D. Conway and H.F. Weinberger, Partial Differential Equations and Dynamical Systems, ed. W. E. Fitzgibbon III (Pitman, Boston, 1984); M. Friedlin, Functional Integration and Partial Differential Equations. Ann. of Math. Studies 109 (Princeton University Press, Princeton, 1985).
38. D.G. Aronson, E.D. Conway and H.F. Weinberger, Partial Differential Equations and Dynamical Systems, ed. W. E. Fitzgibbon III (Pitman, Boston, 1984); M. Friedlin, Functional Integration and Partial Differential Equations. Ann. of Math. Studies 109 (Princeton University Press, Princeton, 1985).
39. S. Koga and Y. Kuramoto, Progr. Theor. Phys. 63 (1980) 106.
40. J. Tyson and J. Keener, Physica D 32 (1988) 327.
41. G. Izús, R. Deza, H. Wio and C. Borzi, Phys. Rev. E, in press.
42. S. Koga, Prog. Theor. Phys. 90 (1993) 1361.
43. H.L. Frisch, V. Privman, C. Nicolis and G. Nicolis, J. Phys. A 23 (1990) 1147.
44. V. Privman and H.L. Frisch, J. Chem. Phys. 94 (1991) 8216.
45. C.R. Doering and J.C. Gadoua, Phys. Rev. Lett. 69 (1992) 2318; U. Zurcher and C.R. Doering, Phys. Rev. E 47 (1993) 3862.
46. C.R. Doering and J.C. Gadoua, Phys. Rev. Lett. 69 (1992) 2318; U. Zurcher and C.R. Doering, Phys. Rev. E 47 (1993) 3862.
47. J.S. Langer, Ann. Phys. 54 (1969) 258.
48. R. Graham and R. Tel, Phys. Rev. Lett. 52 (1984a) 9; R. Graham and R. Tel, J. Stat. Phys. 35 (1984b) 729; R. Graham and R. Tel, Phys. Rev. A 33 (1986) 1322.
49. R. Graham and R. Tel, Phys. Rev. Lett. 52 (1984a) 9; R. Graham and R. Tel, J. Stat. Phys. 35 (1984b) 729; R. Graham and R. Tel, Phys. Rev. A 33 (1986) 1322.
50. R. Graham and R. Tel, Phys. Rev. Lett. 52 (1984a) 9; R. Graham and R. Tel, J. Stat. Phys. 35 (1984b) 729; R. Graham and R. Tel, Phys. Rev. A 33 (1986) 1322.
51. M.P. Hanson, J.Chem.Phys. 60 (1974) 3210.
52. P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley, New York, 1971) p. 17.