Journal of Mathematical Sciences

, Volume 223, Issue 3, pp 285–292 | Cite as

One Numerical Realization of a Generalized Model of World Dynamics and Sustainable Development

  • D. M. Lila
  • A. A. Martynyuk

We present a modification of the Forrester model of world dynamics. A new characteristic that describes the discontent with the development is introduced in each level of the model. It is shown that the proposed model may have a limit cycle.


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  1. 1.
    J. W. Forrester, World Dynamics, Wright–Allen Press, Cambridge (1971).Google Scholar
  2. 2.
    D. L. Meadows and D. H. Meadows, Toward Global Equilibrium, Wright–Allen Press, Cambridge (1972).Google Scholar
  3. 3.
    D. H. Meadows, D. L. Meadows, J. Randers, and W. W. Behrens, The Limits to Growth, University Books, New York (1972).Google Scholar
  4. 4.
    D. H. Meadows, D. L. Meadows, and J. Randers, Beyond the Limits, Chelsea Green Publ. Co., Post Mills (1992).Google Scholar
  5. 5.
    Don. Meadows, J. Randers, and Den. Meadows, Limits to Growth. The 30-Year Update, Chelsea Green Publ. Co., White River Junction (2006).Google Scholar
  6. 6.
    A. A. Martynyuk, “On the one mathematical model of the world dynamics and sustainable development,” Dop. Nats. Akad. Nauk Ukr., No. 7, 16–21 (2010).Google Scholar
  7. 7.
    A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods for the Investigation of Periodic Solutions [in Russian], Vyshcha Shkola, Kiev (1976).Google Scholar
  8. 8.
    P. J. Torres, “Stabilization of optically coupled lasers with periodic pumping,” Nonlin. Oscillat., 14, No. 3, 414–422 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    D.M. Lila and A. A Martynyuk, “On stability of some solutions for equations of locked lasing of optically coupled lasers with periodic pumping,” Nelin. Kolyv., 12, No. 4, 451–460 (2009); English translation: Nonlin. Oscillat., 12, No. 4, 464–473 (2009).Google Scholar
  10. 10.
    A. A. Makhov, Five-Sector Long-Term Macromodel of the World Dynamics Based on the Empirical Data [in Russian], Preprint No. 72, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow (2011).Google Scholar
  11. 11.
    A. V. Korotaev, N. L. Komarova, and D. A. Khalturina, Laws of History. Secular Cycles and Millennial Trends. Demography, Economics, and Wars [in Russian], URSS, Moscow (2007).Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • D. M. Lila
    • 1
  • A. A. Martynyuk
    • 1
  1. 1.Institute of MechanicsUkrainian National Academy of SciencesKievUkraine

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