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Russian Mathematics

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

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

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Abstract

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.

Keywords

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

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References

  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.MATHGoogle Scholar
  2. 2.
    Cooke, K., Yorke, A. Some Equations Modelling Growth Processes and Gonorrhea Epidemics, Math. Biosci. 16, 75–101 (1973).MathSciNetCrossRefMATHGoogle 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].MATHGoogle 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).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bellman, R., Cooke, K. L. Differential-Difference Equations (Academic Press, New York–London, 1963; Mir, Moscow, 1967).MATHGoogle 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].MATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Perm National Research Polytechnic UniversityPermRussia

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