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 (82) ↓ Similar articles (20)

  1. Chun S Journal Of Computational Physics: X 17 100135 (2023)
  2. Chesnokov A A Trudy Matematicheskogo Instituta Imeni V. A. Steklova 322 241 (2023)
  3. Zimovets I V, McLaughlin J A et al Space Sci Rev 217 (5) (2021)
  4. Orlova D V, Danilov V I et al Metals 10 1494 (2020)
  5. Bykov V G Phys Mesomech 23 271 (2020)
  6. Horibe K, Hironaka Ken-ichi et al 29 (9) (2019)
  7. Zykov V S, Bodenschatz E Annu. Rev. Condens. Matter Phys. 9 435 (2018)
  8. Zuev L B, Barannikova S A, Lunev A G Usp. Fiz. Met. 19 379 (2018)
  9. Zuev L  B Metallofiz. Noveishie Tekhnol. 38 1335 (2016)
  10. Osaki K, Satoh H, Yazaki Sh 8 1009 (2015)
  11. Davydov V A, Davydov N V BIOPHYSICS 60 269 (2015)
  12. Chun S J Biol Phys 40 219 (2014)
  13. Löber Ja, Engel H 23 (4) (2013)
  14. Kurkina E S, Semendyaeva N L Comput Math Model 23 133 (2012)
  15. Mironov V A, Smirnov A I, Smirnov L A J. Exp. Theor. Phys. 112 46 (2011)
  16. Wu N, Gao H, Ying H Phys. Rev. E 82 (6) (2010)
  17. Mironov V A, Smirnov L A Bull. Russ. Acad. Sci. Phys. 74 1699 (2010)
  18. Dahlem M A, Hadjikhani N, Ben-Jacob E PLoS ONE 4 e5007 (2009)
  19. Biktasheva I V, Barkley D et al Phys. Rev. E 79 (5) (2009)
  20. Zykov V S Physica D: Nonlinear Phenomena 238 931 (2009)
  21. Vanag V K, Epstein I R 18 (2) (2008)
  22. Schlesner J, Zykov V S et al New J. Phys. 10 015003 (2008)
  23. Schlesner Ja, Zykov V, Engel H Handbook of Chaos Control 1 (2007) p. 591
  24. Kheowan O-U, Davydov V A et al Physics Letters A 367 311 (2007)
  25. Ning-Jie W, Bing-Wei L, He-Ping Y Chinese Phys. Lett. 23 2030 (2006)
  26. Zykov S, Zykov V S, Davydov V Europhys. Lett. 73 335 (2006)
  27. Kantrasiri S, Jirakanjana P, Kheowan O-U Chemical Physics Letters 416 364 (2005)
  28. Gerasev A P Uspekhi Fizicheskikh Nauk 174 1061 (2004)
  29. Zykov V S, Bordiougov G et al Phys. Rev. Lett. 92 (1) (2004)
  30. Kheowan O-U, Uthaisar Ch et al Chemical Physics Letters 399 506 (2004)
  31. Manz N, Steinbock O Phys. Rev. E 70 (6) (2004)
  32. Davydov V A, Morozov V G et al Physics Letters A 325 334 (2004)
  33. Zykov V, Engel H Phys. Rev. E 70 (1) (2004)
  34. Zykov V S, Engel H Physica D: Nonlinear Phenomena 199 243 (2004)
  35. Zhang H, Wu N-J et al 121 7276 (2004)
  36. Guo J-Sh, Ishimura N, Wu Ch-Ch Physica D: Nonlinear Phenomena 198 197 (2004)
  37. Zykov V S, Bordiougov G et al Phys. Rev. E 68 (1) (2003)
  38. Mornev O A, Tsyganov I M et al Jetp Lett. 77 270 (2003)
  39. Davydov V A, Morozov V G, Davydov N V Physics Letters A 307 265 (2003)
  40. Manz N, Davydov V A et al Physics Letters A 316 311 (2003)
  41. Mihaliuk E, Sakurai T et al Phys. Rev. E 65 (6) (2002)
  42. Zykov V S, Engel H Phys. Rev. E 66 (1) (2002)
  43. Davydov V A, Manz N et al Europhys. Lett. 59 344 (2002)
  44. Steinbock O Phys. Rev. Lett. 88 (22) (2002)
  45. Manz N, Davydov V A et al Phys. Rev. E 66 (3) (2002)
  46. Kheowan O-U, Chan Ch-K et al Phys. Rev. E 64 (3) (2001)
  47. Mantel R-M, Barkley D Physica D: Nonlinear Phenomena 149 107 (2001)
  48. Sendiña-Nadal I, Mihaliuk E et al Phys. Rev. Lett. 86 1646 (2001)
  49. Davydov V A, Morozov V G, Davydov N V Physics Letters A 267 326 (2000)
  50. Hoekstra B P T, Diks C G H et al Archives Of Physiology And Biochemistry 108 332 (2000)
  51. Davydov V A, Manz N et al Phys. Rev. Lett. 85 868 (2000)
  52. Merzhanov A G, Rumanov E N Rev. Mod. Phys. 71 1173 (1999)
  53. Yagisita H, Mimura M, Yamada M Physica D: Nonlinear Phenomena 124 126 (1998)
  54. Ikota R, Ishimura N, Yamaguchi T Japan J. Indust. Appl. Math. 15 317 (1998)
  55. Elkin Yu E, Biktashev V N, Holden A V Chaos, Solitons & Fractals 9 1597 (1998)
  56. Zhuravlev V M J. Exp. Theor. Phys. 87 1031 (1998)
  57. Zhuravlev V M Jetp Lett. 65 300 (1997)
  58. Aliev R R, Davydov V A et al J. Phys. Chem. A 101 1313 (1997)
  59. Chernyak Y B, Feldman A B, Cohen R J Phys. Rev. E 55 3215 (1997)
  60. Winfree A T Int. J. Bifurcation Chaos 07 487 (1997)
  61. Gómez-Gesteira M, Mosquera J et al Physics Letters A 231 389 (1997)
  62. Davydov V A, Morozov V G Uspekhi Fizicheskikh Nauk 166 327 (1996)
  63. Comprehensive Chemical Kinetics Vol. Modern Aspects of Diffusion-Controlled Reactions - Cooperative Phenomena in Bimolecular ProcessesChapter 10 General conclusion34 (1996) p. 593
  64. Pérez-Muñuzuri V, Souto C et al Physica D: Nonlinear Phenomena 94 148 (1996)
  65. Grill S, Zykov V S, Müller S C J. Phys. Chem. 100 19082 (1996)
  66. Brazhnik P K, Tyson J J Phys. Rev. E 54 1958 (1996)
  67. Mantel R-M, Barkley D Phys. Rev. E 54 4791 (1996)
  68. Brazhnik P K Physica D: Nonlinear Phenomena 94 205 (1996)
  69. Courtemanche M Chaos, Solitons & Fractals 5 527 (1995)
  70. Nakayama K, Wadati M J. Phys. Soc. Jpn. 64 1501 (1995)
  71. Mikhailov A S, Zykov V S Chemical Waves and Patterns Chapter 4 (1995) p. 119
  72. Kapral R Physica D: Nonlinear Phenomena 86 149 (1995)
  73. Tyson J J, Keener Ja P Chemical Waves and Patterns Chapter 3 (1995) p. 93
  74. Winfree A T Chemical Waves and Patterns Chapter 1 (1995) p. 3
  75. Mikhailov A S Chaos, Solitons & Fractals 5 673 (1995)
  76. Müller S C Muster des Lebendigen Chapter 12 (1994) p. 227
  77. Ito H Physica D: Nonlinear Phenomena 79 16 (1994)
  78. Mikhailov A S, Davydov V A, Zykov V S Physica D: Nonlinear Phenomena 70 1 (1994)
  79. Kotomin E, Kuzovkov V et al J. Phys. A: Math. Gen. 27 1453 (1994)
  80. Steinbock O, Zykov V S, Müller S C Phys. Rev. E 48 3295 (1993)
  81. Cross M C, Hohenberg P C Rev. Mod. Phys. 65 851 (1993)
  82. Steinbock O, Zykov V, Müller S C Nature 366 322 (1993)

© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions