Russian Mathematics

, Volume 61, Issue 4, pp 29–34 | Cite as

On local stability of a population dynamics model with three development stages

  • V. V. MalyginaEmail author
  • M. V. Mulyukov


We consider an age-dependent model of population dynamics, and obtain a sharp effective coefficient criterion of asymptotic stability for the non-trivial equilibrium point.


population dynamics age structure of population delay differential equations stability efficient conditions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pertsev, N. V., Tarasov, I. A. Analysis of Solutions to an Integro-Differential Equation Which Arises in Models of Population Dynamics, Vestn.Omsk.Univ. 2, 13–15 (2003) [in Russian.zbMATHGoogle Scholar
  2. 2.
    Cooke, K., Yorke, A. Some Equations Modelling Growth Processes and Gonorrhea Epidemics, Math. Biosci. 16, 75–101 (1973).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Poluektov, R. A., Pykh, Yu. A., Shvytov, I. A. Dynamic Models of Ecological Systems (Gidrometeoizdat, Leningrad, 1980) [in Russian].Google Scholar
  4. 4.
    Malygina, V. V., Mulyukov, M. V., Pertsev, N. V. On the Local Stability of a Population Dynamics Model with Delay, Sib. È lektron.Mat. Izv. 11, 951–957 (2014) [in Russian].zbMATHGoogle Scholar
  5. 5.
    Malygina, V. V., Sabatulina, T. L. On Stability of a Differential Equation with Aftereffect, Russian Mathematics 58, No. 4, 20–34 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bellman, R., Cooke, K. L. Differential-Difference Equations (Academic Press, New York–London, 1963; Mir, Moscow, 1967).zbMATHGoogle Scholar
  7. 7.
    Elshol’ts, L. E., Norkin, S. B. Introduction to the Theory of Differential Equations with Delay (Nauka, Moscow, 1971) [in Russian].Google Scholar
  8. 8.
    Azbelev, N. V., Maksimov, V. P., Rakhmatullina, L. F. Introduction to the Theory of Functional Differential Equations (Nauka, Moscow, 1991) [in Russian].zbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Perm National Research Polytechnic UniversityPermRussia

Personalised recommendations