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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 12, Pages 2099–2112 (Mi zvmmf4976)  

This article is cited in 31 scientific papers (total in 32 papers)

A modification of Hutchinson's equation

A. Yu. Kolesova, E. F. Mishchenkob, N. Kh. Rozovc

a Faculty of Mathematics, Yaroslavl State University, Sovetskaya ul. 14, Yaroslavl, 150000 Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333 Russia
c Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia

Abstract: A new mathematical object is introduced, namely, a scalar nonlinear delay differential-difference equation is considered that is a modification of Hutchinson's equation, which is well known in ecology. The existence and stability of its relaxation self-oscillations are analyzed.

Key words: differential-difference equation, relaxation cycle, asymptotic behavior, stability.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:12, 1990–2002

Bibliographic databases:

UDC: 519. 624.2
Received: 26.04.2010

Citation: A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “A modification of Hutchinson's equation”, Zh. Vychisl. Mat. Mat. Fiz., 50:12 (2010), 2099–2112; Comput. Math. Math. Phys., 50:12 (2010), 1990–2002

Citation in format AMSBIB
\by A.~Yu.~Kolesov, E.~F.~Mishchenko, N.~Kh.~Rozov
\paper A modification of Hutchinson's equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 12
\pages 2099--2112
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 12
\pages 1990--2002

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    2. A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in systems of delay differential–difference equations in ecology”, Proc. Steklov Inst. Math., 277 (2012), 94–136  mathnet  crossref  mathscinet  isi  elib  elib
    3. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in neural systems”, Comput. Math. Math. Phys., 52:5 (2012), 702–719  mathnet  crossref  mathscinet  isi  elib  elib
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    13. Wu G.-Ch., Baleanu D., “Discrete Chaos in Fractional Delayed Logistic Maps”, Nonlinear Dyn., 80:4, SI (2015), 1697–1703  crossref  mathscinet  isi  scopus
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    18. Azhmyakov V., Ahmed A., Verriest E.I., “On the Optimal Control of Systems Evolving With State Suprema”, 2016 IEEE 55Th Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2016, 3617–3623  isi
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    20. M. M. Preobrazhenskaya, “Relaksatsionnye tsikly v modeli sinapticheski vzaimodeistvuyuschikh ostsillyatorov”, Model. i analiz inform. sistem, 24:2 (2017), 186–204  mathnet  crossref  elib
    21. A. Yu. Perevaryukha, “Razrushenie relaksatsionnykh kolebanii v novoi modeli ekstremalnoi dinamiki chislennosti populyatsii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 55–65  mathnet  crossref
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    24. Verriest E.I., Azhmyakov V., “Advances in Optimal Control of Differential Systems With the State Suprema”, 2017 IEEE 56Th Annual Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2017  isi
    25. Glyzin S.D. Kolesov A.Yu. Marushkina E.A., “Relaxation Oscillations in a System of Two Pulsed Synaptically Coupled Neurons”, Autom. Control Comp. Sci., 51:7 (2017), 658–665  crossref  isi  scopus
    26. Preobrazhenskaia M.M., “Relaxation Cycles in a Model of Synaptically Interacting Oscillators”, Autom. Control Comp. Sci., 51:7 (2017), 783–797  crossref  mathscinet  isi  scopus
    27. Preobrazhenskaia M.M., “The Impulse-Refractive Mode in a Neural Network With Ring Synaptic Interaction”, Autom. Control Comp. Sci., 52:7 (2018), 777–789  crossref  isi  scopus
    28. Azhmyakov V., Verriest E.I., Trujillo L.A.G., Pickl S.W., “On the Optimal Control of Multidimensional Dynamic Systems Evolving With State Suprema”, 2018 IEEE Conference on Decision and Control (Cdc), IEEE Conference on Decision and Control, IEEE, 2018, 61–66  isi
    29. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “A self-symmetric cycle in a system of two diffusely connected Hutchinson's equations”, Sb. Math., 210:2 (2019), 184–233  mathnet  crossref  crossref  adsnasa  isi  elib
    30. Preobrazhenskaia M.M., International Conference on Computer Simulation in Physics and Beyond, Journal of Physics Conference Series, 1163, ed. Shchur L., IOP Publishing Ltd, 2019  crossref  isi
    31. V. E. Goryunov, M. M. Preobrazhenskaya, “Kvaziustoichivost sosuschestvuyuschikh attraktorov neirodinamicheskoi modeli s zapazdyvaniem”, Materialy Voronezhskoi zimnei matematicheskoi shkoly Sovremennye metody teorii funktsii i smezhnye problemy. 28 yanvarya2 fevralya 2019 g. Chast 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 173, VINITI RAN, M., 2019, 26–47  mathnet  crossref
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  •      Computational Mathematics and Mathematical Physics
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