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Model. Anal. Inform. Sist., 2012, Volume 19, Number 3, Pages 32–61 (Mi mais228)  

This article is cited in 11 scientific papers (total in 11 papers)

Asymptotics of Solutions of the Generalized Hutchinson's Equation

S. A. Kaschenko

P. G. Demidov Yaroslavl State University

Abstract: We discuss the dynamics of the Hutchinson's equation and its generalizations. An estimate of the global stability region of a positive steady state is obtained. The main results refer to existence, stability and asymptotics of a slow oscillating solution. New asymptotic methods are applied to a problem of dynamical properties of ODE system describing Belousov–Zhabotinsky reaction.

Keywords: delay differential equation, Hutchinson's equation, large parameter, asymptotic, periodic solution

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Document Type: Article
UDC: 517.9
Received: 20.02.2012

Citation: S. A. Kaschenko, “Asymptotics of Solutions of the Generalized Hutchinson's Equation”, Model. Anal. Inform. Sist., 19:3 (2012), 32–61

Citation in format AMSBIB
\by S.~A.~Kaschenko
\paper Asymptotics of Solutions of the Generalized Hutchinson's Equation
\jour Model. Anal. Inform. Sist.
\yr 2012
\vol 19
\issue 3
\pages 32--61

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    This publication is cited in the following articles:
    1. S. A. Kaschenko, “Relaksatsionnye kolebaniya v sisteme s zapazdyvaniyami, modeliruyuschei zadachu khischnik–zhertva”, Model. i analiz inform. sistem, 20:1 (2013), 52–98  mathnet
    2. N. D. Bykova, S. D. Glyzin, S. A. Kaschenko, “Parametricheskii rezonans pri dvukhchastotnom vozmuschenii v logisticheskom uravnenii s zapazdyvaniem”, Model. i analiz inform. sistem, 20:3 (2013), 86–98  mathnet
    3. S. A. Kaschenko, “Relaksatsionnye kolebaniya v modelyakh mnogovidovykh soobschestv”, Model. i analiz inform. sistem, 20:5 (2013), 5–24  mathnet
    4. I. S. Kashchenko, S. A. Kashchenko, “Dynamics of the logistic delay equation with a large spatially distributed control coefficient”, Comput. Math. Math. Phys., 54:5 (2014), 785–796  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. D. S. Glyzin, S. A. Kashchenko, “Spatially distributed control of the dynamics of the logistic delay equation”, Comput. Math. Math. Phys., 54:6 (2014), 963–976  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. S. A. Kaschenko, “Dinamika logisticheskogo uravneniya s zapazdyvaniem i zapazdyvayuschim upravleniem”, Model. i analiz inform. sistem, 21:5 (2014), 61–77  mathnet
    7. Kashchenko S.A., “Dynamics of the Logistic Equation With Delay and Delay Control”, Int. J. Bifurcation Chaos, 24:8 (2014), 1440017  crossref  mathscinet  zmath  isi  scopus
    8. N. D. Bykova, S. A. Kaschenko, “Korporativnaya dinamika sistem logisticheskikh uravnenii s zapazdyvaniem i s bolshim zapazdyvayuschim upravleniem”, Model. i analiz inform. sistem, 22:3 (2015), 372–391  mathnet  crossref  mathscinet  elib
    9. V. O. Golubenets, “Analiz lokalnykh bifurkatsii dlya uravneniya s zapazdyvaniem, zavisyaschim ot iskomoi funktsii”, Model. i analiz inform. sistem, 22:5 (2015), 711–722  mathnet  crossref  mathscinet  elib
    10. S. A. Kaschenko, D. Loginov, “About Global Stable of Solutions of Logistic Equation With Delay”, VI International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012019  crossref  isi  scopus
    11. S. A. Kashchenko, “Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation”, Math. Notes, 104:2 (2018), 231–243  mathnet  crossref  crossref  isi  elib
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