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Kinematics of autowave structures in excitable media

 a, b, ,
a MIREA - Russian Technological University, prosp. Vernadskogo 78, Moscow, 119454, Russian Federation
b Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation

We consider an approximate approach to the description of complex space-time structures in different types of excitable media based on the kinematics of autowave fronts. Because of the generality and relative simplicity of the kinematic approach, it is possible to obtain analytical results for different types of autowave motion in two and three-dimensional excitable media. The kinematic approach is used to treat steady-state autowave structures and also to study the evolution of autowaves in inhomogeneous, time-dependent and anisotropic media.

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Fulltext is also available at DOI: 10.1070/PU1991v034n08ABEH002462
PACS: 05.65.+b, 05.60.−k, 02.60.Ed (all)
DOI: 10.1070/PU1991v034n08ABEH002462
URL: https://ufn.ru/en/articles/1991/8/b/
Citation: Davydov V A, Zykov V S, Mikhailov A S "Kinematics of autowave structures in excitable media" Sov. Phys. Usp. 34 (8) 665–684 (1991)
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Оригинал: Давыдов В А, Зыков В С, Михайлов А С «Кинематика автоволновых структур в возбудимых средах» УФН 161 (8) 45–85 (1991); DOI: 10.3367/UFNr.0161.199108b.0045

References (130) ↓ Cited by (82) Similar articles (20)

  1. Abramychev A.Yu., Davydov V.A., Zykov B.S. Zh. Eksp. Teor. Fiz. 97 1188 (1990)
  2. Abramychev A.Yu., Davydov V.A., Mikhailov A.S. Biofizika 34 979 (1990)
  3. Agladze K.I., Davydov V.A., Mikhailov A.S. Pis’ma ZhETF 45 601 (1987)
  4. Aranson I.S., Rabinovich M.I. "Dinamika spiral’nykh voln v neravnovesnykh sredakh" Preprint IPF AN SSSR № 212 (Gor’kii, 1988)
  5. Balakhovskii I.S. Biofizika 10 1063 (1965)
  6. Balkarei Yu.I., Nikulin M.G., Elinson M.I. Avtovolnovye Protsessy v Sistemakh s Diffuziei (Gor’kii: IPF AN SSSR, 1981)
  7. Barton V., Kabrera M., Frank F. Elementarnye Protsessy Rosta Kristalla (M.: IL, 1959)
  8. Belousov B.P. Sbornik Referatov Po Radiatsionnoi Meditsine za 1958 G. (M.: Medgiz, 1959) p. 145; to zhe, Belousov B.P. Avtovolnovye Protsessy v Sistemakh s Diffuziei (Gor’kii: IPF AN SSSR, 1981) p. 176
  9. Berkinblit M.B., Kovalev S.A., Smolyaninov V.V., Chailakhyan L.M. Modeli Strukturno-funktsional’noi Organizatsii Nekotorykh Biologicheskikh Sistem (M.: Nauka, 1966) p. 71
  10. Brazhnik P.K., Davydov V.A., Zykov V.S., Mikhailov A.S. Zh. Eksp. Teor. Fiz. 93 1725 (1987)
  11. Brazhnik P.K., Davydov V.A., Mikhailov A.S. Teor. Mat. Fiz. 74 440 (1988)
  12. Brazhnik P.K., Davydov V.A., Mikhailov A.S. Izv. Vuzov. Ser. Radiofizika 32 289 (1989)
  13. Buzdin A.I., Mikhailov A.S. Zh. Eksp. Teor. Fiz. 90 294 (1986)
  14. Vasil’ev V.A., Romanovskii Yu.M., Yakhno V.G. Usp. Fiz. Nauk 128 625 (1979)
  15. Vasil’ev V.A., Romanovskii Yu.M., Yakhno V.G. Avtovolnovye Protsessy (M.: Nauka, 1987)
  16. Vasil’eva A.B., Butuzov V.F. Asimptoticheskie Razlozheniya Reshenii Singulyarno Vozmushchennykh Uravnenii (M.: Nauka, 1973)
  17. Gel’fand I.M., Tsetlin M.L. Dokl. Akad. Nauk SSSR 131 1242 (1960)
  18. Gel’fand S.I., Kazhdan D.L. Dokl. Akad. Nauk SSSR 141 527 (1961)
  19. Gulyaev Yu.V., Kalafati Yu.D., Ryabova L.A., Serbinov I.A Dokl. Akad. Nauk SSSR 256 357 (1981)
  20. Davydov V.A., Zykov V.S. Zh. Eksp. Teor. Fiz. 95 139 (1989)
  21. Davydov V.A., Zykov V.S., Mikhailov A.S., Brazhnik P.K. Izv. Vuzov. Ser. Radiofizika 31 574 (1988)
  22. Davydov V.A., Mikhailov A.S. Nelineinye Volny. Struktury i Bifurkatsii (M.: Nauka, 1987) p. 261
  23. Ermakova E.A., Pertsov A.M., Shnol’ E.E. Dokl. Akad. Nauk SSSR 301 332 (1988)
  24. Zhabotinskii A.M. Kontsentratsionnye Avtokolebaniya (M.: Nauka, 1974)
  25. Zhabotinskii A.M., Otmer X., Fild R. i dr. Kolebaniya i Begushchie Volny v Khimicheskikh Sistemakh (M.: Mir)
  26. Zel’dovich Ya.B. Nelineinye Volny. Rasprostranenie i Vzaimodeistvie (M.: Nauka, 1981) p. 38
  27. Zel’dovich Ya.B., Frank-Kamenetskii D.A. Dokl. Akad. Nauk SSSR 19 693 (1938)
  28. Zykov V. S. Upravlenie Slozhnymi Sistemami (M.: Nauka, 1975) p. 59
  29. Zykov V. S. Biofizika 25 319 (1980)
  30. Zykov V. S. Biofizika 25 888 (1980)
  31. Zykov V. S. Avtovolnovye Protsessy v Sistemakh s Diffuziei (Gor’kii: IPF AN SSSR, 1981) p. 85
  32. Zykov V. S. Modelirovanie Volnovykh Protsessov v Vozbudimykh Sredakh (M.: Nauka, 1984)
  33. Zykov V. S. Biofizika 31 862 (1986)
  34. Zykov V. S. Biofizika 32 337 (1987)
  35. Zykov V. S. Biofizika 34 1031 (1989)
  36. Zykov V.S., Mikhailov A.S. Dokl. Akad. Nauk SSSR 286 341 (1986)
  37. Zykov V.S., Mikhailov A.S. Biofizika 24 717 (1979)
  38. Zykov V.S., Mikhailov A.S. Biofizika 25 1071 (1980)
  39. Zykov V.S., Mikhailov A.S. "Kinematicheskii metod issledovaniya ustoichivosti spiral’nykh avtovoln" Preprint (M.: Institut problem upravleniya AN SSSR, 1988)
  40. Zykov V.S., Morozova O.L., Pratusevich V.P. Voprosy Kibernetiki (93) 43 (1982)
  41. Zykov V.S., Petrov A.A. Biofizika 22 300 (1977)
  42. Ivanitskii G.R., Krinskii V.I., Sel’kov E.E. Matematicheskaya Biofizika Kletki (M.: Nauka, 1978)
  43. Kolmogorov A.N., Petrovskii I.G., Piskunov H.S. Byull. MGU A 1 (6) 1 (1937); to zhe, Kolmogorov A.N., Petrovskii I.G., Piskunov H.S. Voprosy Kibernetiki (12) 3 (1975)
  44. Krinskii V.I. Problemy Kibernetiki (20) 59 (1968)
  45. Krinskii V.I., Medvinskii A.B., Panfilov A.V. Evolyutsiya Avtovolnovykh Vikhrei (M.: Znanie, 1986)
  46. Krinskii V.I., Mikhailov A.S. Avtovolny (M.: Znanie, 1984)
  47. Krinskii V.I., Pertsov A.M., Reshetilov A.H. Biofizika 17 271 (1972)
  48. Kurdyumov S.P., Malinetskii G.G. Sinergetika - Teoriya Samoorganizatsii: Idei, Metody, Perspektivy (M.: Znanie, 1983)
  49. Loskutov A.Yu., Mikhailov A.S. Vvedenie v Sinergetiku (M.: Nauka, 1990)
  50. Mikhailov A.S., Krinskii V.I. Biofizika 27 875 (1982)
  51. Nikolic G., Prigozhii I. Samoorganizatsiya v Neravnovesnykh Sistemakh (M.: Mir, 1979)
  52. Norden A.P. Teoriya Poverkhnostei (M.: Gostekhizdat, 1956)
  53. Ostrovskii L.A., Yakhno V.G. Biofizika 20 489 (1975)
  54. Panfilov A.V., Rudenko A.N., Krinskii V.I. Biofizika 31 850 (1986)
  55. Polak L. S., Mikhailov A. S. Samoorganizatsiya v Neravnovesnykh Fiziko>khimicheskikh Sistemakh (M.: Nauka, 1983)
  56. Rashevskii P.K. Kurs Differentsial’noi Geometrii (M.: Fizmatgiz, 1956)
  57. Romanovskii Yu.M., Stepanova N.V., Chernyavskii D.S. Matematicheskaya Biofizika (M.: Nauka, 1984)
  58. Rudenko A.N., Panfilov A.V. Stud. Biophy. 98 183 (1983)
  59. Svirezhev Yu.M. Nelineinye Volny, Dissipativnye Struktury i Katastrofy v Ekologii (M.: Nauka, 1987)
  60. Skott E. Volny v Aktivnykh i Nelineinykh Sredakh v Prilozhenii v Elektronike (M.: Sov. radio, 1977)
  61. Uizem Dzh. Lineinye i Nelineinye Volny (M.: Mir, 1977)
  62. Frank^Kamenetskii D.A. Diffuziya i Teploperedacha v Khimicheskoi Kinetike (M.: Nauka, 1967)
  63. Khaken G. Sinergetika (M.: Mir, 1980)
  64. Ebeling V. Obrazovanie Struktur pri Neobratimykh Protsessakh (M.: Mir, 1979)
  65. Agladze K.J., Krinsky V.I. Nature 296 424 (1982)
  66. Allessie M.A., Bonke F.J.M., Schopman F.J.G. Circ. Res. 33 54 (1973)
  67. Brower R.C., Kessler D.A., Koplik J., Levins H. Phys. Rev. Lett. 51 1111 (1983)
  68. Brower R.C., Kessler D. A., Koplik J., Levine H. Phys. Rev. A 29 1335 (1984)
  69. Bures J., Koroleva V.I., Gorelova N.A. Self-Organization: Autowaves And Structures Far From Equilibrium (Ed. V.I. Krinsky) (Berlin: Springer-Verlag, 1984) p. 180
  70. Casten R., Cochen H., Langerstrom P. Quart. J. Appl. Math. 32 365 (1975)
  71. Cohen D.S., Neu J.C., Rosales R.R. SIAM J. Appl. Math. 35 536 (1978)
  72. Davidenko J.M., Kent P.P., Chialo D.R., Michaels B.C., Jalife J. "Sustained vortex-like waves in normal isolated ventricular muscle" Reprint (Department of Pharmacology and Physiology SUNY, Health Science Center at Syracuse, 1990)
  73. Davydov V.A., Mikhailov A.S., Zykov V. S. Nonlinear Waves In Active Media (Ed. Yu. Engelbrecht) (Berlin: Springer-Verlag, 1989) p. 38
  74. Davydov V.A., Zykov V.S. Nonlinear World Vol. 1 (Kiev: Naukova Dumka, 1989) p. 81
  75. Dockery J.D., Keener J.P., Tyson J.J. Physica D 30 177 (1988)
  76. Fife P C Non-Equilibrium Dynamics In Chemical Systems (Eds C Vidal, A Pacault) (Berlin: Springer-Verlag, 1984) p. 76
  77. Fife P C J. Stat. Phys. 39 687 (1985)
  78. FitzHugh R Biophys. J. 1 445 (1961)
  79. Foerster P., Muller S.C., Hess V. Science 241 685 (1988)
  80. Gerhardt M., Schuster H., Tyson J.J. Science 247 1563 (1990)
  81. Gerhardt M., Schuster H., Tyson J.J. Physica D 46 392 (1990)
  82. Gerisch G Wilhelm Roux Archiv Entwickelungsmech. Organismen 165 127 (1965)
  83. Gorelova N.A., Bures J. J. Neurobiology 14 353 (1983)
  84. Greenberg J M SIAM J. Appl. Math. 39 301 (1980)
  85. Greenberg J M Adv. Appl. Math. 2 450 (1981)
  86. Hagan P S SIAM J. Appl. Math. 42 762 (1982)
  87. Hramov R.N., Rudenko A.N., Panfilov A.V., Krinsky V.I. Stud. Biophys. 102 69 (1984)
  88. Keener J P SIAM J. Appl. Math. 46 1039 (1986)
  89. Keener J P J. Math. Biol. 26 41 (1988)
  90. Keener J P Physica D 31 269 (1988)
  91. Keener J.P., Tyson J.J. Physica D 21 307 (1986)
  92. Keener J.P., Tyson J.J. Physica D 44 191 (1990)
  93. Kogan B.Ya., Zykov V.S., Petrov A.A. Simulation Of Systems’79 (Amsterdam: North>Holland, 1980) p. 693
  94. Lugosi E Physica D 40 331 (1989)
  95. Markstein G H J. Aeronaut. Sci. 18 199 (1951)
  96. Markus M., Hess B. Dissipative Structures In Transport Processes And Combustion (Berlin: Springer-Verlag, 1990) p. 123
  97. Maselko J., Showalter K. Nature 339 609 (1989)
  98. Meron E Phys. Rev. Lett. 63 684 (1989)
  99. Meron E., Pelce P. Phys. Rev. Lett. 60 1880 (1988)
  100. Mikhailov A.S., Krinsky V.I. Physica D 9 346 (1983)
  101. Mikhailov A.S., Panfilov A.V., Rudenko A.N. Phys. Lett. A 109 246 (1985)
  102. Muller S.C., Plesser T., Hess B. Science 230 661 (1985)
  103. Muller S.C., Plesser T., Hess B. Physica D 24 71 (1987)
  104. Muller S.C., Plesser T., Hess B. Physica D 24 87 (1987)
  105. Nagurno J., Arimoto S., Yoshizawa S. Proc. IRE 50 2061 (1962)
  106. Nandapurkar P.J., Winfree A.T. Physica D 29 69 (1987)
  107. Pertsov A.M., Panfilov A.V., Ermakova E. A. Physica D 14 311 (1984)
  108. Rinzel J., Keller J.B. Biophys. J. 13 1313 (1973)
  109. Rosenblueth A Am. J. Physiol. 194 491 (1958)
  110. Rossler O.E., Kahlert C. Z. Naturforsch. A 34 565 (1979)
  111. Rovinsky A B J. Phys. Chem. 90 217 (1986)
  112. Selfridge O Arch. Inst. Cardiol. Mexico 18 177 (1948)
  113. Skinner G.S., Swinney H.L. Physica D 45 287 (1990)
  114. Sultan R., Ortoleva P.J. J. Chem. Phys. 84 6781 (1986)
  115. Thuring A M Phil. Trans. Roy. Soc. London B 237 37 (1952)
  116. Tyson J.J., Alexander K.A., Manoranjan V.S., Murray J.D. Physica D 34 193 (1989)
  117. Tyson J.J., Keener J.P. Physica D 29 215 (1987)
  118. Tyson J.J., Keener J.P. Physica D 32 327 (1988)
  119. Wiener N., Rosenblueth A. Arch. Inst. Cardiol. Mexico 16 3 (1946)
  120. Winfree A T Science 175 634 (1972)
  121. Winfree A T Science 181 937 (1973)
  122. Winfree A T Sci. Am. 230 (6) 82 (1974)
  123. Winfree A T "The geometry of biological time" Biomathematics Vol. 8 (New York: Springer-Verlag, 1980)
  124. Winfree A T Physica D 12 321 (1984)
  125. Winfree A T When Time Breaks Down (Princeton Univ. Press, 1987)
  126. Winfree A.T., Janke W. J. Phys. Chem. 93 2823 (1989)
  127. Yakushevich L V Stud. Biophys. 100 (3) 195 (1984)
  128. Zaikin A.N., Zhabotinsky A.M. Nature 225 535 (1970)
  129. Zykov V S Simulation Of Wave Processes In Excitable Media (Translation ed. by A.T. Winfree) (Manchester: University Press, 1988)
  130. Zykov V.S., Morozova O.L. Nonlinear Biology 1 (2) 1 (1990)

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