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


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.

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  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.

    MATH  Google Scholar 

  2. 2.

    Cooke, K., Yorke, A. Some Equations Modelling Growth Processes and Gonorrhea Epidemics, Math. Biosci. 16, 75–101 (1973).

    MathSciNet  Article  MATH  Google 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].

    MATH  Google 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).

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Bellman, R., Cooke, K. L. Differential-Difference Equations (Academic Press, New York–London, 1963; Mir, Moscow, 1967).

    Google 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].

    Google Scholar 

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Correspondence to V. V. Malygina.

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Original Russian Text © V.V. Malygina, M.V. Mulyukov, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 4, pp. 35–42.

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Malygina, V.V., Mulyukov, M.V. On local stability of a population dynamics model with three development stages. Russ Math. 61, 29–34 (2017). https://doi.org/10.3103/S1066369X17040053

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