Skip to main content
SpringerLink
Log in

Qualitative study of a class of nonlinear integral models (after V. M. Glushkov)

  • Published:
Cybernetics Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. V. M. Glushkov, V. V. Ivanov, and V. M. Yanenko, “A new class of dynamic models and their applications in biology,” Kibernetika, No. 4, 131–139 (1979); No. 4, 116–125 (1980); No. 5, 113–127 (1981).

    Google Scholar 

  2. V. M. Glushkov, V. V. Ivanov, and Yu. P. Yatsenko, “Analytic study of a class of dynamic models,” Kibernetika, No. 2, 1–12 (1980); No. 3, 104–112 (1982).

    Google Scholar 

  3. Yu. P. Yatsenko, “Modeling certain oscillating biological processes,” Kibernetika, No. 5, 29–35 (1978).

    Google Scholar 

  4. V. V. Ivanov, V. M. Yanenko, Yu. P. Yatsenko, and O. V. Gorda, “Vibrational regimes in a nonlinear integral dynamic model with aftereffect,” in: Ninth International Conference on Nonlinear Vibrations: Abstracts (Kiev, September, 1981) [in Russian], Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1981), pp. 136–137.

    Google Scholar 

  5. A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier, Theory of Bifurcations of Dynamic Systems on a Plane [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  6. V. I. Arnol'd, Additional Chapters to Theory of Ordinary Differential Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  7. A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  8. A. N. Sharkovskii, “Existence of the cycle of continuous transformation of a straight line into itself,” Ukr. Mat. Zh.,16, No. 1, 61–71 (1964).

    Google Scholar 

  9. A. N. Sharkovskii, Difference Equations and Population Size Dynamics [in Russian], Kiev (1982). (Preprint, Inst. Mat. Akad. Nauk Ukr. SSR, No. 82-18.)

  10. J. R. Pounder and T. D. Rogers, “The geometry of chaos: dynamics of nonliner second-order difference equations,” Bull. Math. Biophys.,2, No. 4, 101–121 (1980).

    Google Scholar 

  11. K. Hirai, T. Ushio, and M. Iwai, “Catastrophe and chaos in nonlinear control systems,” in: Ninth International Conference on Nonlinear Vibrations: Abstracts (Kiev, September, 1981), Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1981).

    Google Scholar 

  12. Yu. A. Mitropol'skii and D. I. Martynyuk, Periodic and Quasiperiodic Vibrations of Systems with a Lag [in Russian], Vishcha Shkola, Kiev (1979).

    Google Scholar 

  13. R. L. Clerc and C. Hartmann, “Search of subharmonic resonances of differential equations with periodic coefficients by the method of associated recurrence,” in: Ninth International Conference on Nonlinear Vibrations: Abstracts (Kiev, September, 1981), Inst. Akad. Nauk Ukr. SSR, Kiev (1981).

    Google Scholar 

  14. V. M. Yanenko, “Study of interconnections of vibrational and stochastic regimes in a claclass of dynamic models (after V. M. Glushkov),” in: Third Republic Symposium on Differential Equations: Abstracts (Odessa, June, 1982) [in Russian], Izd. Odessk. Univ., Odessa (1982), pp. 227–229.

    Google Scholar 

  15. G. Matioli and M. Merritt, “Vesudevan stem cell growth and microdiffusion,” Math. Biosci., No. 17, 339–355 (1973).

    Google Scholar 

  16. A. E. Gurvich (ed.), Immunogenesis and Cell Differentiation [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  17. G. I. Marchuk, Mathematical Models in Immunology [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  18. G. I. Marchuk and L. N. Belikh (eds.), Proceedings of the IFIP TC 7 Working Conference on Mathematical Modeling in Immunology and Medicine, North-Holland, Amsterdam (1983).

    Google Scholar 

Download references

Authors
  1. V. V. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Yanenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. P. Yatsenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Kibernetika, No. 4, pp. 110–115, July–August, 1983.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, V.V., Yanenko, V.M. & Yatsenko, Y.P. Qualitative study of a class of nonlinear integral models (after V. M. Glushkov). Cybern Syst Anal 19, 576–584 (1983). https://doi.org/10.1007/BF01068347

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01068347

Keywords

Search

Navigation