Population Explosions

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


A possible mechanism for the self-organization of complex patterns is the selective amplification of some fluctuation modes provided by external noise. This situation is naturally realized if we have a distributed system that undergoes explosive development from some unstable stationary state. A particular example (and one that is very important for applications) is explosive population growth in fluctuating media. We show in this chapter that such growth results in the formation of very complex intermittent patterns, where small regions with greatly enhanced population density randomly alternate with larger regions that are sparsely populated. We shall also investigate the explosion threshold in different types of fluctuating media.


Stochastic Differential Equation Ignition Time Creation Rate Breeding Center Spherical Spreading 
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  1. 10.1
    Ya.B. Zeldovich: Dokl. Akad. Nauk SSSR 257, 1173 (1981)Google Scholar
  2. 10.2
    Ya.B. Zeldovich, A.S. Mikhailov: Sov. Phys. Usp. 30, 977 (1988)ADSCrossRefGoogle Scholar
  3. 10.3
    A.S. Mikhailov: Phys. Rep. 184, 307–374 (1989)ADSCrossRefGoogle Scholar
  4. 10.4
    A.N. Kolmogorov, I.E. Petrovskii, N.S-Piskunov: Bul. Mosk. Univ. Mat. Mekh. 1, 1 (1937)Google Scholar
  5. 10.5
    R.A. Fisher: Ann. Eugenics 7, 355 (1937)CrossRefGoogle Scholar
  6. 10.6
    A.N. Kolmogorov: Izv. Akad. Nauk SSSR. Mat. No. 3, 355 (1937)Google Scholar
  7. 10.7
    Ya.B. Zeldovich, S.A. Molchanov, A.A. Ruzmaikin, D.D. Sokolov: Sov. Phys. Usp. 30, 353 (1987)MathSciNetADSCrossRefGoogle Scholar
  8. 10.8
    D.D. Sokolov, T.S. Shumkina: Vestn. Mosk. Univ. Fiz. Astron. 29, 23 (1988)MathSciNetGoogle Scholar
  9. 10.9
    L.D. Landau, E.M. Lifshitz: Quantum Mechanics. Nonrelativistic Theory (Pergamon, Oxford 1977) p. 45Google Scholar
  10. 10.10
    A.S. Mikhailov, I.V. Uporov: Sov. Phys. JETP 57, 863 (1983)Google Scholar
  11. 10.11
    A.S. Mikhailov, I.V. Uporov: Sov. Phys. Usp. 27, 695 (1984)ADSCrossRefGoogle 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

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