• Alexander S. Mikhailov
  • Alexander Yu. Loskutov
Part of the Springer Series in Synergetics book series (SSSYN, volume 52)


Interactions between elements in distributed active systems can produce a great variety of different patterns, either stationary or time-dependent. The process of their spontaneous formation is known as self-organization. In the first volume of this book we described typical coherent structures in active media, such as self-propagating fronts and pulses, spiral waves, localized stationary dissipative patterns, etc. We also discussed the coherent behavior of neural and reproductive networks. The second volume deals mainly with much more complex chaotic patterns that are also found in distributed active systems.


Strange Attractor External Noise Spiral Wave Structural Hierarchy Coherent Pattern 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.1
    E. Lorenz: J. Atm. Sci. 20, 130–141 (1963)ADSCrossRefGoogle Scholar
  2. 1.2
    Ya.G. Sinai: Dokl. Akad. Nauk SSSR 153, 1261–1264 (1963)Google Scholar
  3. 1.3
    B.A. Huberman, J.P. Crutchfield, N.H. Packard: Appl. Phys. Lett. 37, 750–752 (1980)ADSCrossRefGoogle Scholar
  4. 1.4
    D. Ruelle, F. Takens: Commun. Math. Phys. 20, 167–192 (1971)MathSciNetADSCrossRefzbMATHGoogle Scholar
  5. 1.5
    A.J. Lichtenberg, M.A. Lieberman: Regular and Stochastic Motion (Springer, Berlin, Heidelberg 1983)zbMATHGoogle Scholar
  6. 1.6
    H.G. Schuster: Deterministic Chaos (Physik-Verlag, Weinheim, 1984)zbMATHGoogle Scholar
  7. 1.7
    G.M. Zaslavskii: Stochasticity of Dynamical Systems (Nauka, Moscow 1984)zbMATHGoogle Scholar
  8. 1.8
    K. Kaneko: Physica D34, 1–41 (1989)ADSGoogle Scholar
  9. 1.9
    W. Feller: An Introduction to Probability Theory and its Applications, Vols. 1 and 2 (Wiley, New York 1968 and 1971)zbMATHGoogle Scholar
  10. 1.10
    L. Arnold: Stochastic Differential Equations: Theory and Applications (Wiley, New York 1974)zbMATHGoogle Scholar
  11. 1.11
    Z. Schuss: Theory and Applications of Stochastic Differential Equations (Wiley, New York 1980)zbMATHGoogle Scholar
  12. 1.12
    N.G. van Kampen: Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam 1983)Google Scholar
  13. 1.13
    R.L. Stratonovich: Topics in the Theory of Random Noise, Vols. I and II (Gordon and Breach, New York 1963 and 1967)Google Scholar
  14. 1.14
    C.W. Gardiner: Handbook of Stochastic Methods (Springer, Berlin, Heidelberg 1985)Google Scholar
  15. 1.15
    H. Risken: The Fokker-Planck Equation, 2nd ed. (Springer, Berlin, Heidelberg 1989)CrossRefzbMATHGoogle Scholar
  16. 1.16
    W. Horsthemke, R.L. Lefever: Noise-Induced Transitions (Springer, Berlin, Heidelberg 1984)zbMATHGoogle Scholar
  17. 1.17
    R. Thorn: Structural Stability and Morphogenesis (Benjamin, Reading 1975)Google Scholar
  18. 1.18
    V.I. Arnold: Catastrophe Theory (Springer, Berlin, Heidelberg 1986)Google Scholar
  19. 1.19
    H.A. Ceccatto, B.A. Huberman: Physica Scripta 37, 145–150 (1988)MathSciNetADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alexander S. Mikhailov
    • 1
    • 2
  • Alexander Yu. Loskutov
    • 1
  1. 1.Department of PhysicsMoscow State UniversityMoscowUSSR
  2. 2.Institut für Theoretische Physik und SynergetikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

Personalised recommendations