Abonnement à la biblothèque: Guest
Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections
Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337

Volume 51, 2019 Volume 50, 2018 Volume 49, 2017 Volume 48, 2016 Volume 47, 2015 Volume 46, 2014 Volume 45, 2013 Volume 44, 2012 Volume 43, 2011 Volume 42, 2010 Volume 41, 2009 Volume 40, 2008 Volume 39, 2007 Volume 38, 2006 Volume 37, 2005 Volume 36, 2004 Volume 35, 2003 Volume 34, 2002 Volume 33, 2001 Volume 32, 2000 Volume 31, 1999 Volume 30, 1998 Volume 29, 1997 Volume 28, 1996

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.

Articles with similar content:

Localized Wave Structures in Nonequilibrium Media
Journal of Automation and Information Sciences, Vol.44, 2012, issue 11
Vyacheslav A. Danylenko , Sergey I. Skuratovskiy
Singularities of Manifolds of Stationary States of Dynamic Systems under Change of Control Parameters
Journal of Automation and Information Sciences, Vol.31, 1999, issue 4-5
V. G. Verbitsky
On Periodizing Solution of Dynamical Systems with the Simplest Symmetry under Changing of Control Parameters. Part 1
Journal of Automation and Information Sciences, Vol.31, 1999, issue 7-9
Leonid G. Lobas
Differential Games of Fractional Order with Impulse Effect
Journal of Automation and Information Sciences, Vol.47, 2015, issue 4
Ivan I. Matychyn, Victoriya V. Onyshchenko
Optimal Sets of Practical Stability of Differential Inclusions
Journal of Automation and Information Sciences, Vol.35, 2003, issue 3
Fedor G. Garashchenko, Vladimir V. Pichkur