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 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 322 241 (2023)
  5. Zimovets I V, McLaughlin J A et al Space Sci Rev 217 (5) (2021)
  6. Orlova D V, Danilov V I et al Metals 10 (11) 1494 (2020)
  7. Bykov V G Phys Mesomech 23 (3) 271 (2020)
  8. Horibe K, Hironaka Ken-ichi 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. Davydov V A, Davydov N V BIOPHYSICS 60 (2) 269 (2015)
  13. Osaki K, Satoh H, Yazaki Sh DCDS-S 8 (5) 1009 (2015)
  14. Chun S J Biol Phys 40 (3) 219 (2014)
  15. Löber Ja, 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. Biktasheva I V, Barkley D et al Phys. Rev. E 79 (5) (2009)
  22. Dahlem M A, Hadjikhani N, Ben-Jacob E PLoS ONE 4 (4) e5007 (2009)
  23. Zykov V S Physica D: Nonlinear Phenomena 238 (11-12) 931 (2009)
  24. Vanag V K, Epstein I R Chaos: An Interdisciplinary Journal of Nonlinear Science 18 (2) (2008)
  25. Schlesner J, Zykov V S et al New J. Phys. 10 (1) 015003 (2008)
  26. Schlesner Ja, Zykov V, Engel H Handbook of Chaos Control 1 (2007) p. 591
  27. Kheowan O-U, Davydov V A et al Physics Letters A 367 (4-5) 311 (2007)
  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. Gerasev A P Uspekhi Fizicheskikh Nauk 174 (10) 1061 (2004)
  32. Kheowan O-U, Uthaisar Ch et al Chemical Physics Letters 399 (4-6) 506 (2004)
  33. Guo J-Sh, Ishimura N, Wu Ch-Ch Physica D: Nonlinear Phenomena 198 (3-4) 197 (2004)
  34. Manz N, Steinbock O Phys. Rev. E 70 (6) (2004)
  35. Zhang H, Wu N-J et al The Journal of Chemical Physics 121 (15) 7276 (2004)
  36. Davydov V A, Morozov V G et al Physics Letters A 325 (5-6) 334 (2004)
  37. Zykov V S, Engel H Physica D: Nonlinear Phenomena 199 (1-2) 243 (2004)
  38. Zykov V, Engel H Phys. Rev. E 70 (1) (2004)
  39. Zykov V S, Bordiougov G et al Phys. Rev. Lett. 92 (1) (2004)
  40. Davydov V A, Morozov V G, Davydov N V Physics Letters A 307 (5-6) 265 (2003)
  41. Manz N, Davydov V A et al Physics Letters A 316 (5) 311 (2003)
  42. Zykov V S, Bordiougov G et al Phys. Rev. E 68 (1) (2003)
  43. Mornev O A, Tsyganov I M et al Jetp Lett. 77 (6) 270 (2003)
  44. Mihaliuk E, Sakurai T et al Phys. Rev. E 65 (6) (2002)
  45. Steinbock O Phys. Rev. Lett. 88 (22) (2002)
  46. Davydov V A, Manz N et al Europhys. Lett. 59 (3) 344 (2002)
  47. Manz N, Davydov V A et al Phys. Rev. E 66 (3) (2002)
  48. Zykov V S, Engel H Phys. Rev. E 66 (1) (2002)
  49. Mantel R-M, Barkley D Physica D: Nonlinear Phenomena 149 (1-2) 107 (2001)
  50. Sendiña-Nadal I, Mihaliuk E et al Phys. Rev. Lett. 86 (8) 1646 (2001)
  51. Kheowan O-U, Chan Ch-K et al Phys. Rev. E 64 (3) (2001)
  52. Davydov V A, Manz N et al Phys. Rev. Lett. 85 (4) 868 (2000)
  53. Hoekstra B P T, Diks C G H et al Archives Of Physiology And Biochemistry 108 (4) 332 (2000)
  54. Davydov V A, Morozov V G, Davydov N V Physics Letters A 267 (5-6) 326 (2000)
  55. Morozov V G, Davydov N V, Davydov V A Journal Of Biological Physics 25 (2-3) 87 (1999)
  56. Elkin Yu E, Biktashev V N Journal Of Biological Physics 25 (2-3) 129 (1999)
  57. Merzhanov A G, Rumanov E N Rev. Mod. Phys. 71 (4) 1173 (1999)
  58. Yagisita H, Mimura M, Yamada M Physica D: Nonlinear Phenomena 124 (1-3) 126 (1998)
  59. Ikota R, Ishimura N, Yamaguchi T Japan J. Indust. Appl. Math. 15 (2) 317 (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. Zhuravlev V M Jetp Lett. 65 (3) 300 (1997)
  63. Aliev R R, Davydov V A et al J. Phys. Chem. A 101 (7) 1313 (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. Chernyak Y B, Feldman A B, Cohen R J Phys. Rev. E 55 (3) 3215 (1997)
  67. Brazhnik P K, Tyson J J Phys. Rev. E 54 (2) 1958 (1996)
  68. Pérez-Muñuzuri V, Souto C et al Physica D: Nonlinear Phenomena 94 (3) 148 (1996)
  69. Grill S, Zykov V S, Müller S C J. Phys. Chem. 100 (49) 19082 (1996)
  70. Mantel R-M, Barkley D Phys. Rev. E 54 (5) 4791 (1996)
  71. Davydov V A, Morozov V G Uspekhi Fizicheskikh Nauk 166 (3) 327 (1996)
  72. Brazhnik P K Physica D: Nonlinear Phenomena 94 (4) 205 (1996)
  73. Comprehensive Chemical Kinetics Vol. Modern Aspects of Diffusion-Controlled Reactions - Cooperative Phenomena in Bimolecular ProcessesChapter 10 General conclusion34 (1996) p. 593
  74. Nakayama K, Wadati M J. Phys. Soc. Jpn. 64 (5) 1501 (1995)
  75. Courtemanche M Chaos, Solitons & Fractals 5 (3-4) 527 (1995)
  76. Mikhailov A S Chaos, Solitons & Fractals 5 (3-4) 673 (1995)
  77. Mikhailov A S, Zykov V S Chemical Waves and Patterns Chapter 4 (1995) p. 119
  78. Tyson J J, Keener Ja P Chemical Waves and Patterns Chapter 3 (1995) p. 93
  79. Kapral R Physica D: Nonlinear Phenomena 86 (1-2) 149 (1995)
  80. Winfree A T Chemical Waves and Patterns Chapter 1 (1995) p. 3
  81. Mikhailov A S, Davydov V A, Zykov V S Physica D: Nonlinear Phenomena 70 (1-2) 1 (1994)
  82. Ito H Physica D: Nonlinear Phenomena 79 (1) 16 (1994)
  83. Müller S C Muster des Lebendigen Chapter 12 (1994) p. 227
  84. Kotomin E, Kuzovkov V et al J. Phys. A: Math. Gen. 27 (5) 1453 (1994)
  85. Steinbock O, Zykov V S, Müller S C Phys. Rev. E 48 (5) 3295 (1993)
  86. Cross M C, Hohenberg P C Rev. Mod. Phys. 65 (3) 851 (1993)
  87. Steinbock O, Zykov V, Müller S C Nature 366 (6453) 322 (1993)

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