Issues

 / 

1991

 / 

August

  

Reviews of topical problems


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.

Fulltext pdf (1.1 MB)
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)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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 (87) ↓ Similar articles (20)

  1. Chun S Springer Asia Pacific Mathematics Series Vol. Moving Frames for the Numerical Solution of Partial Differential Equations in Complex DomainsRelative Acceleration and the Riemann Curvature Tensor7 Chapter 6 (2026) p. 207
  2. Chun S Journal Of Computational Physics: X 17 100135 (2023)
  3. Bykov V G IJG 14 (01) 108 (2023)
  4. Chesnokov A A ’nру’?ы ’a’?т’?’?’?т’?ch’?с’?’?’?’? ’?’?ст’?тут’? ’?’?’?’?’? ’E. ’B. ’lт’?’?’?’?’?’? 322 241 (2023)
  5. Zimovets I V, McLaughlin J A et al Space Sci Rev 217 (5) (2021)
  6. Bykov V G Phys Mesomech 23 (3) 271 (2020)
  7. Orlova D V, Danilov V I et al Metals 10 (11) 1494 (2020)
  8. Horibe K, Hironaka K-i et al Chaos: An Interdisciplinary Journal of Nonlinear Science 29 (9) (2019)
  9. Zuev L B, Barannikova S A, Lunev A G Usp. Fiz. Met. 19 (4) 379 (2018)
  10. Zykov V S, Bodenschatz E Annu. Rev. Condens. Matter Phys. 9 (1) 435 (2018)
  11. Zuev L  B Metallofiz. Noveishie Tekhnol. 38 (10) 1335 (2016)
  12. Osaki K, Satoh H, Yazaki Sh DCDS-S 8 (5) 1009 (2015)
  13. Davydov V A, Davydov N V BIOPHYSICS 60 (2) 269 (2015)
  14. Chun S J Biol Phys 40 (3) 219 (2014)
  15. Löber Jakob, Engel H Chaos: An Interdisciplinary Journal of Nonlinear Science 23 (4) (2013)
  16. Kurkina E S, Semendyaeva N L Comput Math Model 23 (2) 133 (2012)
  17. Mironov V A, Smirnov A I, Smirnov L A J. Exp. Theor. Phys. 112 (1) 46 (2011)
  18. Wu N, Gao H, Ying H Phys. Rev. E 82 (6) (2010)
  19. Zuev L B, Barannikova S A JMP 01 (01) 1 (2010)
  20. Mironov V A, Smirnov L A Bull. Russ. Acad. Sci. Phys. 74 (12) 1699 (2010)
  21. Dahlem M A, Hadjikhani N, Ben-Jacob E PLoS ONE 4 (4) e5007 (2009)
  22. Biktasheva I V, Barkley D et al Phys. Rev. E 79 (5) (2009)
  23. Zykov V S Physica D: Nonlinear Phenomena 238 (11-12) 931 (2009)
  24. Schlesner J, Zykov V S et al New J. Phys. 10 (1) 015003 (2008)
  25. Vanag V K, Epstein I R Chaos: An Interdisciplinary Journal of Nonlinear Science 18 (2) (2008)
  26. Kheowan O-U, Davydov V A et al Physics Letters A 367 (4-5) 311 (2007)
  27. Schlesner Ja, Zykov V, Engel H Handbook of Chaos Control 1 (2007) p. 591
  28. Zykov S, Zykov V S, Davydov V Europhys. Lett. 73 (3) 335 (2006)
  29. Ning-Jie W, Bing-Wei L, He-Ping Y Chinese Phys. Lett. 23 (8) 2030 (2006)
  30. Kantrasiri S, Jirakanjana P, Kheowan O-U Chemical Physics Letters 416 (4-6) 364 (2005)
  31. Manz N, Steinbock O Phys. Rev. E 70 (6) (2004)
  32. Zykov V S, Engel H Physica D: Nonlinear Phenomena 199 (1-2) 243 (2004)
  33. Davydov V A, Morozov V G et al Physics Letters A 325 (5-6) 334 (2004)
  34. Zykov V S, Bordiougov G et al Phys. Rev. Lett. 92 (1) (2004)
  35. Gerasev A P Uspekhi Fizicheskikh Nauk 174 (10) 1061 (2004)
  36. Guo J-Sh, Ishimura N, Wu Ch-Ch Physica D: Nonlinear Phenomena 198 (3-4) 197 (2004)
  37. Kheowan O-U, Uthaisar Ch et al Chemical Physics Letters 399 (4-6) 506 (2004)
  38. Zykov V, Engel H Phys. Rev. E 70 (1) (2004)
  39. Zhang H, Wu N-J et al The Journal of Chemical Physics 121 (15) 7276 (2004)
  40. Manz N, Davydov V A et al Physics Letters A 316 (5) 311 (2003)
  41. Zykov V S, Bordiougov G et al Phys. Rev. E 68 (1) (2003)
  42. Davydov V A, Morozov V G, Davydov N V Physics Letters A 307 (5-6) 265 (2003)
  43. Mornev O A, Tsyganov I M et al Jetp Lett. 77 (6) 270 (2003)
  44. Davydov V A, Manz N et al Europhys. Lett. 59 (3) 344 (2002)
  45. Manz N, Davydov V A et al Phys. Rev. E 66 (3) (2002)
  46. Mihaliuk E, Sakurai T et al Phys. Rev. E 65 (6) (2002)
  47. Zykov V S, Engel H Phys. Rev. E 66 (1) (2002)
  48. Steinbock O Phys. Rev. Lett. 88 (22) (2002)
  49. Kheowan O-U, Chan Ch-K et al Phys. Rev. E 64 (3) (2001)
  50. Sendiña-Nadal Irene, Mihaliuk E et al Phys. Rev. Lett. 86 (8) 1646 (2001)
  51. Mantel R-M, Barkley D Physica D: Nonlinear Phenomena 149 (1-2) 107 (2001)
  52. Davydov V A, Morozov V G, Davydov N V Physics Letters A 267 (5-6) 326 (2000)
  53. Davydov V A, Manz N et al Phys. Rev. Lett. 85 (4) 868 (2000)
  54. Hoekstra B P T, Diks C G H et al Archives Of Physiology And Biochemistry 108 (4) 332 (2000)
  55. Merzhanov A G, Rumanov E N Rev. Mod. Phys. 71 (4) 1173 (1999)
  56. Elkin Yu E, Biktashev V N Journal Of Biological Physics 25 (2-3) 129 (1999)
  57. Morozov V G, Davydov N V, Davydov V A Journal Of Biological Physics 25 (2-3) 87 (1999)
  58. Ikota R, Ishimura N, Yamaguchi T Japan J. Indust. Appl. Math. 15 (2) 317 (1998)
  59. Yagisita H, Mimura M, Yamada M Physica D: Nonlinear Phenomena 124 (1-3) 126 (1998)
  60. Zhuravlev V M J. Exp. Theor. Phys. 87 (5) 1031 (1998)
  61. Elkin Yu E, Biktashev V N, Holden A V Chaos, Solitons & Fractals 9 (9) 1597 (1998)
  62. Aliev R R, Davydov V A et al J. Phys. Chem. A 101 (7) 1313 (1997)
  63. Chernyak Y B, Feldman A B, Cohen R J Phys. Rev. E 55 (3) 3215 (1997)
  64. Gómez-Gesteira M, Mosquera J et al Physics Letters A 231 (5-6) 389 (1997)
  65. Winfree A T Int. J. Bifurcation Chaos 07 (03) 487 (1997)
  66. Zhuravlev V M Jetp Lett. 65 (3) 300 (1997)
  67. Pérez-Muñuzuri V, Souto C ’? ’?р Physica D: Nonlinear Phenomena 94 (3) 148 (1996)
  68. Grill S, Zykov V S, Müller S C J. Phys. Chem. 100 (49) 19082 (1996)
  69. Brazhnik P K, Tyson J J Phys. Rev. E 54 (2) 1958 (1996)
  70. Mantel R-M, Barkley D Phys. Rev. E 54 (5) 4791 (1996)
  71. Brazhnik P K Physica D: Nonlinear Phenomena 94 (4) 205 (1996)
  72. Davydov V A, Morozov V G ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 166 (3) 327 (1996)
  73. Comprehensive Chemical Kinetics Vol. Modern Aspects of Diffusion-Controlled Reactions - Cooperative Phenomena in Bimolecular ProcessesChapter 10 General conclusion34 (1996) p. 593
  74. Courtemanche M Chaos, Solitons & Fractals 5 (3-4) 527 (1995)
  75. Mikhailov A S Chaos, Solitons & Fractals 5 (3-4) 673 (1995)
  76. Winfree A T Chemical Waves and Patterns Chapter 1 (1995) p. 3
  77. Kapral R Physica D: Nonlinear Phenomena 86 (1-2) 149 (1995)
  78. Nakayama K, Wadati M J. Phys. Soc. Jpn. 64 (5) 1501 (1995)
  79. Mikhailov A S, Zykov V S Chemical Waves and Patterns Chapter 4 (1995) p. 119
  80. Tyson J J, Keener Ja P Chemical Waves and Patterns Chapter 3 (1995) p. 93
  81. Ito H Physica D: Nonlinear Phenomena 79 (1) 16 (1994)
  82. Müller Stefan C Muster des Lebendigen Chapter 12 (1994) p. 227
  83. Kotomin E, Kuzovkov V et al J. Phys. A: Math. Gen. 27 (5) 1453 (1994)
  84. Mikhailov A S, Davydov V A, Zykov V S Physica D: Nonlinear Phenomena 70 (1-2) 1 (1994)
  85. Steinbock O, Zykov V, Müller Stefan C Nature 366 (6453) 322 (1993)
  86. Steinbock O, Zykov V S, Müller S C Phys. Rev. E 48 (5) 3295 (1993)
  87. Cross M C, Hohenberg P C Rev. Mod. Phys. 65 (3) 851 (1993)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions