Criteria of spontaneous interconversions of traveling and static arbitrary dimensional dissipative structures

Physica D: Nonlinear Phenomena

Volumn 93, Issue 3-4, 1996, Pages 143-156

  Osipov, V V ^a  

^a Federal State Unitary Enterprise   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001538811     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00296-0     Document Type: Article

References (79)

1. G. Nicolis and I. Prigogine, Self-Organization in Non-equilibrium Systems (Wiley, New York, 1977).
2. H. Haken, Synergetics (Springer, Berlin, 1977).
3. V.A. Vasil'ev, Yu.M. Pomanovskii and V.G. Yahno, Autowave Processes in Kinetic Systems (VEB Deutscher Verlag der Wissenschaften, Berlin, 1987).
4. B.N. Belintsev, Usp. Fiz. Nauk 141 (1983) 55
5. [Sov. Phys. Usp. 26 (1983) 775].
6. R.J. Fielder and M. Burger, ed., Oscillations and Traveling Waves in Chemical Systems (Wiley, New York, 1985).
7. B.S. Kerner and V.V. Osipov, Mikroelektronika Akad. Nauk SSSR 14 (1985) 389;
8. Autosolitons, in: Nonlinear Irreversible Processes, eds. W. Ebeling and H. Ulbricht, Springer Series in Synergetics, Ser. 33. B. (Springer, Berlin, 1986).
9. B.S. Kerner and V.V. Osipov, Usp. Fiz. Nauk 160 (1990) 1
10. [Sov. Phys. Usp. 33 (1990) 3].
11. M.C. Cross and P.S. Hohenberg, Rev. Mod. Phys. 65 (1993) 851.
12. B.S. Kerner and V.V. Osipov, Autosolitons: A New Approach to Problem of Self-Organization and Turbulence (Kluwer, Academic Publishers, Dordrecht, 1994) [in Russian: Nauka, Moscow, 1991].
13. B.S. Kerner and V.V. Osipov, Usp. Fiz. Nauk 157 (1989) 201
14. [Sov. Phys. Usp. 32 (1989) 101].
15. B.S. Kerner and V.V. Osipov, Thermal diffusion autosolitons in semiconductors and gas plasmas, in: Nonlinear Waves 1: Dynamics and Evolution (Springer, Berlin, 1989).
16. B.S. Kerner and V.V. Osipov, Zh. Eksp. Teor. Fiz. 89 (1985) 589
17. [Sov. Phys. JETP 62 (1985) 337].
18. A.M. Zhabotinskii, Concentration Oscillations (Nauka, Moscow, 1974).
19. K.J. Lee, W.D. McCormick, Q. Ouyong and H.L. Swinney, Science 261 (1993) 189.
20. P. Gray and S. Scott, Chem. Eng. Sci. 38 (1983) 29;
21. P. Gray and S. Scott, Chem. Eng. Sci. 39 (1984) 1087;
22. J. Phys. Chem. 89 (1985) 22.
23. A. Gierer and H. Meinhardt, Kybernetik 12 (1972) 30;
24. H. Meinhardt and A. Gierer, J. Cell. Sci. 15 (1974) 321.
25. J. Rinzel and J.B. Keller, Biophys. J. 13 (1973) 1313;
26. J. Rinzel and D. Ferman, SIAM J. Appl. Math. 42 (1982) 1111.
27. P.G. FitzHugh, Biophys. J. 1 (1961) 445;
28. J. Nagumo, S. Yoshizawa and S. Arimoto, IEEE Trans. Circuit Theory st-12 (1965) 400.
29. P.J. Ortoleva and J. Ross, J. Chem. Phys. 63 (1975) 3398;
30. P. Ortoleva and R. Suitan, J. Chem. Phys. 148 (1990) 47.
31. R.G. Casten, H. Cohen and A. Lagerstrom, Quart. Appl. Math. 32 (1975) 365.
32. S. Koga and Y. Kuramoto, Prog. Theor. Phys. 63 (1980) 106.
33. G.B. Ermentrout, S.P. Hastings and W.C. Troy, SIAM J. Appl. Math. 44 (1984) 1133.
34. G.A. Klaasen and W.C. Troy, SIAM J. Appl. Math. 44 (1984) 1133.
35. G.A. Klaasen, Rocky Mountain J. Math. 16 (1986) 119.
36. A.T. Winfree, Science 175 (1972) 634;
37. A.T. Winfree, Science 181 (1973) 937.
38. B.S. Kerner and V.V. Osipov, Zh. Eksp. Teor. Fiz. 74 (1978) 1675
39. [Sov. Phys. JETP 47 (1978) 874];
40. Fiz. Tekh. Poluprovod. 13 (1979) 721
41. [Sov. Phys. Semicond. 13 (1979) 424].
42. B.S. Kerner and V.V. Osipov, Zh. Eksp. Teor. Fiz. 79 (1980) 2218
43. [Sov. Phys. JETP 52 (1980) 1122].
44. A. Hagberg and E. Meron, Phys. Rev. Lett. 72 (1994) 2492.
45. N. Wiener and A. Rosenblueth, Arch. Inst. Cardiologia de Mexico 16 (1946) 205.
46. T. Ohta, M. Mimura and R. Kobayashi, Physica D 34 (1989) 115.
47. W.N. Reynolds, J.E. Pearson and S. Ponce-Dawson, Phys. Rev. Lett. 72 (1994) 2797.
48. V.V. Osipov, Phys. Rev. E 48 (1993) 88.
49. I.A. Lubashevskii and V.V. Gafiichuk, Phys. Rev. E 50 (1994) 171;
50. D.M. Petrich and R.E. Goldstein, Phys. Rev. Lett. 72 (1994) 1120.
51. B.S. Kerner, E.M. Kuznetsova and V.V. Osipov, Mikroelektronika Akad. Nauk SSSR 13 (1984) 407, 456;
52. Dok. Akad. Nauk SSSR 277 (1984) 1114
53. [Sov. Phys. Dok. 29 (1984) 664].
54. A. Ito and T. Ohta, Phys. Rev. A 45 (1992) 8374.
55. K. Krisher and A. Mikhailov, Phys. Rev. Lett. 73 (1994) 3163.
56. E.M. Kuznetsova and V.V. Osipov, Phys. Rev. E 51 (1995) 148.
57. B.S. Kerner and V.V. Osipov, Mikroelektronika Akad. Nauk SSSR 10 (1981) 408.
58. P.C. Fife, J. Chem. Phys. 64 (1976) 554;
59. J. Math. Anal. Appl. 54 (1976) 497.
60. B.S. Kerner and V.V. Osipov, Mikroelektronika Akad. Nauk SSSR 12 (1983) 512.
61. J.D. Dockery and J.P. Keener, SIAM J. Appl. Math. 49 (1989) 539.
62. B.S. Kerner and V.V. Osipov, Zh. Eksp. Teor. Fiz. 83 (1982) 2201
63. [Sov. Phys. JETP 56 (1982) 1275].
64. V.V. Gafiichuk, B.S. Kerner, I.M. Lazurchak and V.V. Osipov, Mikroelektronika Akad. Nauk SSSR 15 (1986) 180.
65. V.V. Osipov, V.V. Gafiichuk, B.S. Kerner and I.M. Lazurchak, Mikroelektronika Akad. Nauk SSSR 16 (1987) 23.
66. V.V. Gafiichuk, V.E. Gashpar, B.S. Kerner and V.V. Osipov, Fiz. Tekh. Poluprovod. 22 (1988) 1836
67. [Sov. Phys. Semicond. 22 (1988) 1298].
68. T. Ohta, A. Ito and A. Tetsuka, Phys. Rev. A 42 (1990) 3225.
69. H. Willebrand, K. Matthiessen, F.J. Niedernostheide, R. Dohmen and H.G. Purwins, Contr. Plasma Phys. 32 (1992) 57.
70. H. Willebrand, T. Hunteier, F.J. Niedernostheide, R. Dohmen and H.G. Purwins, Phys. Rev. A 45 (1992) 8766.
71. G.N. Barenblatt and Ya.B. Zel'dovich, Prikl. Mat. Mekh. 21 (1957) 865.
72. L.D. Landau and E.M. Lifshitz, Hydrodynamics (Nauka, Moscow, 1986)
73. [Fluid Mechanics (Pergamon, Oxford, 1959)].
74. D.D. Joseph, Stability of Pluid Motions (Springer, Berlin, 1976).
75. G. Iooss and D.D. Joseph, Elementary Stability and Bifurcation Theory (Springer, Berlin, 1980).
76. Y. Nishiura and M. Mimura, SIAM J. Appl. Math. 49 (1989) 481;
77. A. Arneodo, J. Elezgaray, J. Pearson and T. Russo, Physica D 49 (1991) 141.
78. V.V. Osipov and C.B. Muratov, Phys. Rev. E 50 (1994) 3251.
79. V.V. Osipov and C.B. Muratov, Phys. Rev. Lett. 75 (1995) 338.