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Modelirovanie i Analiz Informatsionnykh Sistem, 2012, Volume 19, Number 3, Pages 32–61 (Mi mais228)  

This article is cited in 16 scientific papers (total in 16 papers)

Asymptotics of Solutions of the Generalized Hutchinson's Equation

S. A. Kaschenko

P. G. Demidov Yaroslavl State University
References:
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.
Received: 20.02.2012
Document Type: Article
UDC: 517.9
Language: Russian
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
\Bibitem{Kas12}
\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
\mathnet{http://mi.mathnet.ru/mais228}
Linking options:
  • https://www.mathnet.ru/eng/mais228
  • https://www.mathnet.ru/eng/mais/v19/i3/p32
  • This publication is cited in the following 16 articles:
    1. S. V. Aleshin, D. S. Glyzin, S. A. Kaschenko, “Wave propagation in the Kolmogorov–Petrovsky–Piscounov–Fisher equation with delay”, Theoret. and Math. Phys., 220:3 (2024), 1411–1428  mathnet  crossref  crossref  mathscinet  adsnasa
    2. V. E. Goryunov, “Dynamics of solutions of logistic equation with delay and diffusion in a planar domain”, Theoret. and Math. Phys., 212:2 (2022), 1092–1110  mathnet  crossref  crossref  mathscinet  adsnasa
    3. V. O. Golubenets, “Relaxation oscillations in a logistic equation with past state-dependent delay”, Theoret. and Math. Phys., 207:3 (2021), 738–750  mathnet  crossref  crossref  adsnasa  isi  elib
    4. V. O. Golubenets, “Relaxation Oscillations in a Logistic Equation with Nonconstant Delay”, Math. Notes, 107:6 (2020), 920–932  mathnet  crossref  crossref  mathscinet  isi  elib
    5. V. E. Goryunov, “Osobennosti vychislitelnoi realizatsii algoritma otsenki lyapunovskikh pokazatelei sistem s zapazdyvaniem”, Model. i analiz inform. sistem, 26:4 (2019), 572–582  mathnet  crossref
    6. 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  mathscinet  isi  elib
    7. 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
    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. 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
    11. 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
    12. S. A. Kaschenko, “Dinamika logisticheskogo uravneniya s zapazdyvaniem i zapazdyvayuschim upravleniem”, Model. i analiz inform. sistem, 21:5 (2014), 61–77  mathnet
    13. 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
    14. S. A. Kaschenko, “Relaksatsionnye kolebaniya v sisteme s zapazdyvaniyami, modeliruyuschei zadachu «khischnik–zhertva»”, Model. i analiz inform. sistem, 20:1 (2013), 52–98  mathnet
    15. 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
    16. S. A. Kaschenko, “Relaksatsionnye kolebaniya v modelyakh mnogovidovykh soobschestv”, Model. i analiz inform. sistem, 20:5 (2013), 5–24  mathnet
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