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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i9.20
pages 25-37

Investigation of Uniform by Delay Stability of Nontrivial Equilibrium Point of One Population Model

Bedrik Puzha
Brno University of Technology, Brno
Denis Ya. Khusainov
Kiev National Taras Shevchenko University, Kiev
Veronika Novotna
Brno University of Technology, Brno
Andrey V. Shatyrko
Kiev National Taras Shevchenko University, Ukraine


Consideration was given to a mathematical model of population dynamics in the form of a system of two differential equations with a time delay argument and a quadratic right-hand side. The corresponding system without delay was preliminary studied and its phase portrait was constructed. The effect of delay on the qualitative behavior of solutions was considered. Using the Lyapunov direct method there was studied the stability of nonzero stationary equilibrium state. The results are formulated in the form of matrix algebraic inequalities.


  1. Volterra V., Mathematical theory of struggle for existence [Russian translation], Nauka, Moscosw, 1976.

  2. Smith J. Maynard, Models in ecology, University Press, Cambridge, 1974.

  3. Gopalsamy K., Stability and oscillations in delay differential equations of population dynamics, Kluver Academic Publ., Dortrecht, Boston, London, 1992.

  4. El’sgol’ts L.E., Norkin S.B., Introduction to the theory of the differential equations with deviating argument, Academic Press, New York, 1973.

  5. Hale J., Theory of functional differential equations, Springer-Verlag, New York, 1977.

  6. Demidovich B.P., Lectures on mathematical theory of motion stability [in Russian], Nauka, Moscow, 1967.

  7. Khusainov D.Ya., Shatyrko A.V., Lyapunov functions method in studying stability of differential- functional systems [in Russian], Izdatelstvo KGU, Kiev, 1997.

  8. Davidov V., Khusainov D., Stability investigation of quadratic systems with delay, Journal of Applied Mathematics and Analysis, 2000, 13, No. 1, 85–92.

  9. Martynyuk A.A., Khusainov D.Ya., Chernienko V.A., Constructive estimation of Lyapunov function for the systems with quadratic right nonlinearity, Prikladnaya mekhanika, 2018, 54, No. 3, 114–126.

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