Kinematics of autowave structures in excitable media

Soviet Physics - Uspekhi

Volumn 34, Issue 8, 1991, Pages 665-684

  Davydov, V A ^a,b   Zykov, V S ^a,b   Mikhailov, A S ^a,b  

^a MIREA RUSSIAN TECHNOLOGICAL UNIVERSITY   (Russian Federation)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84931472342     PISSN: 00385670     EISSN: 21695296     Source Type: Journal    
DOI: 10.1070/PU1991v034n08ABEH002462     Document Type: Article

References (166)

1. Abramychev Yu A, Davydov V A and Zykov V S 1990 Zh. Eksp. Teor. Fiz. 97 1188
2. Abramychev Yu A, Davydov V A and Zykov V S 1990 Sov. Phys. JETP 70 666
3. Abramychev Yu A, Davydov V A and Mikhailov A S 1990 Biofizika 34 979
4. Abramychev Yu A, Davydov V A and Mikhailov A S 1990 Biophys. J. 34
5. Agladze K I, Davydov V A and Mikhailov A S 1987 Pis'ma Zh. Eksp. Teor. Fiz. 45 601
6. Agladze K I, Davydov V A and Mikhailov A S 1987 JETP Lett. 45 767
7. Aranson I S and Rabinovich M I 1988 Dynamics of spiral waves in nonuniform media ArXiv e-print IAP, No. 212
8. Balakhovskii I S 1965 Biofizika 10 1063
9. Balakhovskii I S 1965 Biophys. J. 10 1175
10. Balkarei Yu I, Nikulin M G and Elinson M I 1981 Autowave Processes in Systems with Diffusion (IAP, Gor'kii) (in Russian)
11. Barton W, Cabrera M and Frank F 1959 Elementary Processes of Crystal Growth (IL, M.) Russ. transl.
12. Belousov V P 1958 Sbornik Referat. Radiats. Meditsin. (Medgiz., M.) (In Russian)
13. Belousov V P 1981 Autowave Processes in Systems with Diffusion (IAP, Gor'kii) (in Russian)
14. Berkinblum M B, Kovalev S A, Smolyaninov V V and Chailakhyan L M 1966 Models of Structural and Functional Organization of Biological Systems (Nauka, M.) p 71 (in Russian)
15. Brazhnik P K, Davydov V A, Zykov V S and Mikhailov A S 1987 Zh. Eksp. Teor. Fiz. 93 1725
16. Brazhnik P K, Davydov V A, Zykov V S and Mikhailov A S 1987 Sov. Phys. JETP 66 984
17. Brazhnik P K, Davydov V A and Mikhailov A S 1988 Teor. Mat. Fiz. 74 440
18. Brazhnik P K, Davydov V A and Mikhailov A S 1988 Theor. Math. Phys. 74 300
19. Brazhnik P K, Davydov V A and Mikhailov A S 1989 Izv. Vyssh. Uchebn. Zaved. Radiofiz. 32 289
20. Brazhnik P K, Davydov V A and Mikhailov A S 1989 Radiophys. Quantum Electron. 32
21. Buzdin A I and Mikhailov A S 1986 Zh. Eksp. Teor. Fiz. 90 294
22. Buzdin A I and Mikhailov A S 1986 Sov. Phys. JETP 63 169
23. Vasil'ev V A, Romanovskii Yu M and Yakhno V G 1979 Usp. Fiz. Nauk 128 625
24. Vasil'ev V A, Romanovskii Yu M and Yakhno V G 1979 Sov. Phys. Usp. 22 615
25. Vasil'ev V A, Romanovskii Yu M and Yakhno V G 1987 Autowave Processes (Nauka, M.) (in Russian)
26. Vasil'eva A B and Butuzov V F 1973 Asymptotic Expansions of the Solutions of Singular Perturbed Equations (Nauka, M.) (in Russian)
27. Gel'fand I M and Tsetlin M L 1960 Dokl. Akad. Nauk SSSR 131 1242
28. Gel'fand I M and Tsetlin M L 1960 Sov. Math. Dokl. 1
29. Gel'fand S I and Kazhdan D A 1961 Dokl. Akad. Nauk SSSR 141 527
30. Gel'fand S I and Kazhdan D A 1961 Sov. Math. Dokl. 2
31. Gulyaev Yu V, Kalafati Yu D, Ryabova L A and Serbinov I A 1981 Dokl. Akad. Nauk SSSR 256 357
32. Gulyaev Yu V, Kalafati Yu D, Ryabova L A and Serbinov I A 1981 Sov. Phys. Dokl. 26 52
33. Davydov V A and Zykov V S 1989 Zh. Eksp. Teor. Fiz. 95 139
34. Davydov V A and Zykov V S 1989 Sov. Phys. JETP 68 80
35. Davydov V A, Zykov V S, Mikhailov A S and Brazhnik P K 1988 Izv. Vyssh. Uchebn. Zaved. Radiofiz. 31 574
36. Davydov V A, Zykov V S, Mikhailov A S and Brazhnik P K 1988 Radiophys. Quantum Electron. 31
37. Davydov V A and Mikhailov A S 1987 Nonlinear Waves. Structures and Bifurcation (Nauka, M.) (in Russian)
38. Ermakova E A, Pertsov A M and Shnol L L 1988 Dokl. Akad. Nauk SSSR 301 332
39. Ermakova E A, Pertsov A M and Shnol L L 1988 Sov. Phys. Dokl. 33 519
40. Zhabotinskii A M 1974 Concentration Self-Excited Oscillations (Nauka, M.) (in Russian)
41. Zhabotinskii A M, Otmer K, Field R et al 1974 Oscillations and Travelling Waves in Chemical Systems
42. Zhabotinskii A M, Otmer K, Field R et al 1974 Oscillations and Travelling Waves in Chemical Systems (Mir, M.) Russ. transl.
43. Zel'dovich Ya B 1981 Nonlinear Waves. Propagation and Interaction, (Nauka, M.) p 38 (In Russian)
44. Zel'dovich Ya B and Frank-Kamenetskii D A 1938 Dokl. Akad. Nauk SSSR 19 693
45. Zykov V S 1975 Control of Complex Systems (Nauka, M.) p 59 (in Russian)
46. Zykov V S 1980 Biofizika 25 319
47. Zykov V S 1980 Biophys. J. 25 329
48. Zykov V S 1980 Biofizika 25 888
49. Zykov V S 1980 Biophys. J. 25 906
50. Zykov V S 1981 Autowave Processes in Systems with Diffusion (IAP, Gor'kii) p 85 (in Russian)
51. Zykov V S 1984 Simulation of Wave Processes in Excitable Media (Nauka, M.) (in Russian)
52. Zykov V S 1986 Biofizika 31 862
53. Zykov V S 1986 Biophys. J. 31 940
54. Zykov V S 1987 Biofizika 32 337
55. Zykov V S 1987 Biophys. J. 32 365
56. Zykov V S 1989 Biofizika 34 1031
57. Zykov V S 1989 Biophys. J. 34 1114
58. Zykov V S and Mikhailov A S 1986 Dokl. Akad. Nauk SSSR 286 341
59. Zykov V S and Mikhailov A S 1986 Sov. Phys. Dokl. 31 51
60. Zykov V S and Morozova O L 1979 Biofizika 24 717
61. Zykov V S and Morozova O L 1979 Biophys. J. 24 739
62. Zykov VS and OMorozova L 1980 Biofizika 25 1071
63. Zykov VS and OMorozova L 1980 Biophys. J. 25 1100
64. Zykov V S and Morozova O L 1988 The kinematic treatment of the stability of spiral autowaves ArXiv e-print (Inst, of Problems in Control, Moscow)
65. Zykov V S, Morozova O L and Pratusevich V R 1982 Vopr. Kibern. (93) 43
66. Zykov V S and Petrov A A 1977 Biofizika 22 300
67. Zykov V S and Petrov A A 1977 Biophys. J. 22 307
68. Ivanitskii G R, Krinskii V I and Sel'kov E E 1978 Mathematical Biophysics of Cells (Nauka, M.) (in Russian)
69. Kolmogorov A N, Petrovskii I G and Piskunov N S 1937 Byull. Mosk. Univ. Sek. A 1 (6) 1
70. Kolmogorov A N, Petrovskii I G and Piskunov N S 1975 Vopr. Kibern. (12) 3
71. Krinskii V I 1968 Probl. Kibern. (20) 59
72. Krinskii B I, Medvinskii A B and Panfilov A V 1968 Evolution of Autowave Vortices (Znanie, M.) (in Russian)
73. Krinskii V I and Mikhailov A S 1984 Autowaves (Znanie, M.) (in Russian)
74. Krinskii V I, Pertsov A M and Reshetilov A N 1972 Biofizika 17 271
75. Krinskii V I, Pertsov A M and Reshetilov A N 1972 Biophys. J. 17 282
76. Kurdyumov S P and Malinetskii G G 1983 Synergetics: The Theory of Self-Organization. Ideas, Methods, and Perspectives (Znanie, M.) (in Russian)
77. Doskutov Yu A and Mikhailov A S 1990 Introduction to Synergetics (Nauka, M.) (in Russian)
78. Mikhailov A S and VKrinskii I 1982 Biofizika 27 875
79. Mikhailov A S and VKrinskii I 1982 Biophys. (USSR) 27 919
80. Nicolis G and Prigogine I 1977 Self-Organization in Non-Equilibrium Systems (Wiley, N.Y.)
81. Nicolis G and Prigogine I 1979 Self-Organization in Non-Equilibrium Systems (Mir, M.) Russ. transl.
82. Norden A P 1956 Theory of Surfaces (Gostekhizdat, M.) (in Russian)
83. Ostrovskii L A and Yakhno V G 1975 Biofizika 20 489
84. Ostrovskii L A and Yakhno V G 1975 Biophys. J. 20 498
85. Panfilov A V, Rudenko A N and Krinskii V I 1986 Biofizika 31 850
86. Panfilov A V, Rudenko A N and Krinskii V I 1986 Biophys. J. 31 926
87. Polak L S and Mikhailov A S 1983 Self-Organization in Nonequilibrium Physical and Chemical Systems (Nauka, M.) (in Russian)
88. Rashevskil P K 1956 Course of Differential Geometry (Fizmatgiz, M.) (in Russian)
89. Romanovskii Yu M, Stepanova N V and Chernavskii D S 1984 Mathematical Biophysics (Nauka, M.) (in Russian)
90. Rudenko A N and Panfilov A V 1983 Stud. Biophy. 98 183
91. Svirezhev Yu M 1987 Nonlinear Waves, Dissipative Structures, and Catastrophes in Ecology (Nauka, M.) (in Russian)
92. Scott E 1987 Waves in Active and Nonlinear Media in Electronics
93. Scott E 1977 Waves in Active and Nonlinear Media in Electronics (Sov. Radio, Moscow) Russian translation.
94. Whitham G B 1974 Linear and Nonlinear Waves (Wiley Interscience, N.Y.)
95. Whitham G B 1977 Linear and Nonlinear Waves (Mir, M.) Russ. transl.
96. Frank-Kamenetskii D A 1967 Diffusion and Heat Transfer in Chemical Kinetics (Nauka, M.) (in Russian)
97. Haken H 1977 Introduction to Synergetics (Springer-Verlag, N.Y.)
98. Haken H 1980 Introduction to Synergetics (Mir, M.) Russ. transl.
99. Ebeling W 1976 Strukturbildung Bei Irreversiblen Prozessen (Teubner, Leipzig) (in German)
100. Ebeling W 1979 Strukturbildung Bei Irreversiblen Prozessen (Mir, M.) Russ. transl.
101. Agladze K I and Krinsky V I 1982 Nature (London) 296 424
102. Allessie M A, Bonke F I M and Schopman F J G 1973 Circ. Res. 33 54
103. Brower R C, Kessler D A, Koplik J and Levine H 1983 Phys. Rev. Lett. 51 1111
104. Brower R C, Kessler D A, Koplik J and Levine H 1984 Phys. Rev. A 29 1335
105. Bures J, Koroleva V I and Gorelova N A 1984 Self-Organization: Autowaves and Structures far from Equilibrium Ed V I Krinsky (Springer-Verlag Berlin) p 180
106. Casten R, Cochen H and Langerstrom P 1975 Quart. J. Appl. Math. 32 365
107. Cohen D S, Neu J C and Rosales R R 1978 SIAM J. Appl. Math. 35 536
108. Davidenko J M, Kent P F, Chialo D R, Michaels D C and Jalife J 1990 Sustained vortex-like waves in normal isolated ventricular muscle Reprint (Dept. of Pharmacology and Physiology, SUNY, Health Science Center at Syracuse, NY)
109. Davydov V A, Mikhailov A S and Zykov V S 1989 Nonlinear Waves in Active Media ed by Yu Engelbrecht (Springer-Verlag, Berlin) p 38
110. Davydov V A and Zykov V S 1989 Nonlinear World vol 1 (Naukova Dumka, Kiev) p 81
111. Dockery J D, Keener J P and Tyson J J 1988 Physica D 30 177
112. Fife P C 1984 Non-Equilibrium Dynamics in Chemical Systems ed C Vidal and A Pacault (Springer-Verlag, Berlin) p 76
113. Fife P C 1985 J. Stat. Phys. 39 687
114. FitzHugh R 1961 Biophys. J. 1 445
115. Foerster P, Muller S C and Hess B 1988 Science 241 685
116. Gerhardt M, Schuster H and Tyson J J 1990 Science 247 1563
117. Gerhardt M, Schuster H and Tyson J J 1990 Physica D 46 392
118. Gerisch G 1965 Wilhelm Roux Archiv Entwickelungsmech. Organismen 165 127
119. Gorelova N A and Bures J 1983 J. Neurobiology 14 353
120. Greenberg J M 1980 SIAM J. Appl. Math. 39 301
121. Greenberg J M 1981 Adv. Appl. Math. 2 450
122. Hagan P S 1982 SIAM J. Appl. Math. 42 762
123. Hramov R N, Rudenko A N, Panfilov A V and Krinsky V I 1984 Stud. Biophys. 102 69
124. Keener J P 1986 SIAM J. Appl. Math. 46 1039
125. Keener J P 1988 J. Math. Biol. 26 41
126. Keener J P 1988 Physica D 31 269
127. Keener J P and Tyson J J 1986 Physica D 21 307
128. Keener J P and Tyson J J 1990 Physica D 44 191
129. Kogan Ya B, Zykov V S and Petrov A A 1980 Simulation of Systems 79 (North-Holland, Amsterdam) p 693
130. Lugosi E 1989 Physica D 40 331
131. Markstein G H 1951 J. Aeronaut. Sci. 18 199
132. Markus M and Hess B 1990 Dissipative Structures in Transport Processes and Combustion (Springer-Verlag, Berlin) p 123
133. Maselko J and Showalter K 1989 Nature (London) 339 609
134. Meron E 1989 Phys. Rev. Lett. 63 684
135. Meron E and Pelce P 1988 Phys. Rev. Lett. 60 1880
136. Mikhailov A S and Krinsky V J 1983 Physica D 9 346
137. Mikhailov A S, Panfilov A V and Rudenko A N 1985 Phys. Lett. A 109 246
138. Muller S C, Plesser T and Hess B 1985 Science 230 661
139. Muller S C, Plesser T and Hess B 1987 Physica D 24 71
140. Muller S C, Plesser T and Hess B 1987 Physica D 24 87
141. Nagumo J, Arimoto S and Yoshizawa S 1962 Proc. IRE 50 2061
142. Nandapurkar P J and Winfree A T 1987 Physica D 29 69
143. Pertsov A M, Panfilov A V and Ermakova E A 1984 Physica D 14 311
144. Rinzel J and Keller J B 1973 Biophys. J. 13 1313
145. Rosenblueth A 1958 Am. J. Physiol. 194 491
146. Rossler O E and Kahlert C 1979 Z. Naturforsch. Teil A 34 565
147. Rovinsky A B 1986 J. Phys. Chem. 90 217
148. Selfridge O 1948 Arch. Inst. Cardiol. Mexico 18 177
149. Skinner G S and Swinney H L 1990 Physica D 45 287
150. Sultan R and Ortoleva P J 1986 J. Chem. Phys. 84 6781
151. Thuring A M 1952 Phil. Trans. R. Soc. (London) B 237 37
152. Tyson J J, Alexander K A, Manoranjan V S and Murray J D 1989 Physica D 34 193
153. Tyson J J and Keener J P 1987 Physica D 29 215
154. Tyson J J and Keener J P 1988 Physica D 32 327
155. Wiener N and Rosenblueth A 1946 Arch. Inst. Cardiol. Mexico 16 3
156. Winfree A T 1972 Science 175 634
157. Winfree A T 1973 Science 181 937
158. Winfree A T 1974 Sci. Am. 230 (6) 82
159. Winfree A T 1980 The geometry of biological time Biomathematics vol 8 (Springer-Verlag, N.Y.)
160. Winfree A T 1984 Physica D 12 321
161. Winfree A T 1987 When Time Breaks Down (Princeton Univ. Press)
162. Winfree A T and Janke W 1989 J. Phys. Chem. 93 2823
163. Yakushevich L V 1984 Stud. Biophys. 100 (3) 195
164. Zaikin A N and Zhabotinsky A M 1970 Nature (London) 225 535
165. Zykov V S 1988 Simulation of Wave Processes in Excitable Media ed by A T Winfree (Univ. Press, Manchester)
166. Zykov V S and Morozova O L 1990 Nonlinear Biology 1 (2) 1