Advertisement

Oscillatory Media

  • Alexander S. Mikhailov
Part of the Springer Series in Synergetics book series (SSSYN, volume 51)

Abstract

Oscillatory media represent a continuous limit of a large population of self-oscillating elements, with weak interactions between the neighbors. Since interactions between the neighboring elements are weak, they cannot significantly change the amplitude and the form of individual oscillations. Therefore such interactions are principally manifested in changes of the oscillation phases. This notion allows one to construct an approximate description of processes in oscillatory media in terms of phase variables.

Keywords

Rotation Frequency Excitable Medium Topological Charge Phase Dynamic Spiral Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 4.1
    G.B. Whitham: J. Fluid Mech. 44, 373 (1970)CrossRefzbMATHADSMathSciNetGoogle Scholar
  2. 4.2
    Y. Kuramoto: Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, Heidelberg 1984)CrossRefzbMATHGoogle Scholar
  3. 4.3
    L.N. Howard, N. Kopell: Stud. Appl. Math. 56, 95–146 (1977)zbMATHADSMathSciNetGoogle Scholar
  4. 4.4
    N. Kopell, L.N. Howard: Stud. Appl. Math. 64, 1–56 (1981)zbMATHMathSciNetGoogle Scholar
  5. 4.5
    Y. Kuramoto: Prog. Theor. Phys. Suppl. 64, 346–362 (1978)CrossRefADSGoogle Scholar
  6. 4.6
    G.I. Sivashinsky: Ann. Rev. Fluid Mech. 15, 179–199 (1983)CrossRefADSGoogle Scholar
  7. 4.7
    M.C. Cross: “Theoretical methods in pattern formation in physics, chemistry and biology” in Far from Equilibrium Phase Transitions, ed. by L. Garrido (Springer, Berlin, Heidelberg 1988) pp. 45-74Google Scholar
  8. 4.8
    Y. Kuramoto, T. Tsuzuki: Prog. Theor. Phys. 55, 356–369 (1976)CrossRefADSGoogle Scholar
  9. 4.9
    E.M. Lifshitz, L.P. Pitaevskii: Course of Theoretical Physics. Vol.10. Physical Kinetics (Nauka, Moscow 1979) Chap. 12Google Scholar
  10. 4.10
    A.S. Mikhailov, I.V. Uporov: Dokl. Akad. Nauk SSSR 249, 733–736 (1979)Google Scholar
  11. 4.11
    Ya.B. Zeldovich, B.A. Malomed: Dokl. Akad. Nauk SSSR 254, 92–94 (1980)MathSciNetGoogle Scholar
  12. 4.12
    Y. Kuramoto: Prog. Theor. Phys. 63, 1885–1895 (1980)CrossRefzbMATHADSMathSciNetGoogle Scholar
  13. 4.13
    N. Kopell, L.N. Howard: Science 180, 1171–1173 (1973)CrossRefADSGoogle Scholar
  14. 4.14
    P. Ortoleva, J. Ross: J. Chem. Phys. 58, 5673 (1973)CrossRefADSGoogle Scholar
  15. 4.15
    J.C. Neu: SIAM J. Appl. Math. 36, 509 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 4.16
    J.C. Neu: SIAM J. Appl. Math. 38, 305 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 4.17
    B.A. Malomed: Z. Phys. 55, 241–248, 249-256 (1984)CrossRefMathSciNetGoogle Scholar
  18. 4.18
    A.N. Zaikin, A.M. Zhabotinskii: Nature 225, 535–538 (1970)CrossRefADSGoogle Scholar
  19. 4.19
    K.I. Agladze, V.I. Krinsky: “On the mechanism of target pattern formation in the distributed Belousov-Zhabotinsky system” in Self-Organization: Autowaves and Structures far from Equilibrium, ed. by V.I. Krinsky (Springer, Berlin, Heidelberg 1984) pp. 147–149CrossRefGoogle Scholar
  20. 4.20
    J.J. Tyson, P.C. Fife: J. Chem. Phys. 73, 2224–2236 (1980)CrossRefADSMathSciNetGoogle Scholar
  21. 4.21
    J.J. Tyson: J. Chim. Physique 84, 1359–1365 (1987)MathSciNetGoogle Scholar
  22. 4.22
    Sh. Bose, Su. Bose, P. Ortoleva: J. Chem. Phys. 72, 4258 (1980)CrossRefADSGoogle Scholar
  23. 4.23
    V.G. Yakhno: Biofizika 20, 669–675 (1975)Google Scholar
  24. 4.24
    V.A. Vasilev, Yu.M. Romanovskii, D.S. Chernavskii, V.G. Yakhno: Autowave Processes in Kinetic Systems (Reidel, Dordrecht 1986) Chap. 5Google Scholar
  25. 4.25
    G.T. Gurija, M.A. Livshits: Phys. Lett. 97A, 175–177 (1983)ADSMathSciNetGoogle Scholar
  26. 4.26
    V.A. Vasilev, M.S. Polyakova: Vestnik MGU. Ser. Fizika 16, 99–104 (1975)Google Scholar
  27. 4.27
    L.D. Landau, E.M. Lifshitz: Course of Theoretical Physics. Vol.3. Quantum Mechanics (Pergamon, Oxford 1977)Google Scholar
  28. 4.28
    A.S. Mikhailov, A. Engel: Phys. Lett. 117A 257–260 (1986)ADSGoogle Scholar
  29. 4.29
    D.S. Cohen, J.C. Neu, R.R. Rosales: SIAM J. Appl. Math. 35, 536–549 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 4.30
    T. Erneux, M. Herchkowitz-Kaufman: Bull. Math. Biol. 41, 767–782 (1979)zbMATHMathSciNetGoogle Scholar
  31. 4.31
    J.M. Greenberg: SIAM J. Appl. Math. 39, 301–309 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  32. 4.32
    J.M. Greenberg: Adv. Appl. Math. 2, 450 (1981)CrossRefzbMATHGoogle Scholar
  33. 4.33
    Ya.B. Zeldovich, B.A. Malomed: Izv. VUZ. Radiofizika 25, 591–618 (1982)ADSMathSciNetGoogle Scholar
  34. 4.34
    P.S. Hagan: SIAM J. Appl. Math. 42, 762–781 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  35. 4.35
    B.A. Malomed: Dokl. Akad. Nauk SSSR 291, 327–332 (1986)MathSciNetGoogle Scholar
  36. 4.37
    S. Koga: Prog. Theor. Phys. 67, 164 (1982)CrossRefzbMATHADSMathSciNetGoogle Scholar
  37. 4.38
    S. Koga: Prog. Theor. Phys. 67, 454–463 (1982)CrossRefzbMATHADSMathSciNetGoogle Scholar
  38. 4.39
    I.S. Aranson, M.I. Rabinovich: J. Phys. 22A, (1989)Google Scholar
  39. 4.40
    I.S. Aranson, M.I. Rabinovich: Izv. VUZ. Radiofizika 29, 1514–1517 (1986)ADSMathSciNetGoogle Scholar
  40. 4.41
    Bodenschatz, A. Weber, L. Kramer: “Dynamics and pattern of spiral waves and defects in travelling waves” in Nonlinear Wave Processes in Excitable Media, ed. by A.V. Holden, M. Markus, H.G. Othmer (Plenum Press, New York 1990) in pressGoogle Scholar
  41. 4.42
    C. Elphick, E. Meron: Localized and Extended Patterns in Reactive Media, Proc. IMA Workshop on Patterns and Dynamics in Reactive Media, Minneapolis (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Alexander S. Mikhailov
    • 1
  1. 1.Department of PhysicsMoscow State UniversityMoscowUSSR

Personalised recommendations