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Model. Anal. Inform. Sist., 2009, Volume 16, Number 3, Pages 96–115 (Mi mais67)  

This article is cited in 13 scientific papers (total in 13 papers)

Difference approximations of “reaction–diffusion” equation on a segment

S. D. Glyzin

P. G. Demidov Yaroslavl State University

Abstract: The system of phase differences for a chain of diffuse weakly coupled oscillators on a stable integral manifold is constructed and analysed. It is shown by means of numerical methods that as the number of oscillators in the chain increases, the Lyapunov dimention growth is close to linear. The extensive computations performed for difference model of Ginsburg-Landau equation illustrate this result and determine the applicability limits for asymptotic methods.

Keywords: chaotic attractor, autooscillations, autogenerator, Lyapunov's dimension, bifurcations, invariant torus

Full text: PDF file (538 kB)
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UDC: 517.9
Received: 22.09.2009

Citation: S. D. Glyzin, “Difference approximations of “reaction–diffusion” equation on a segment”, Model. Anal. Inform. Sist., 16:3 (2009), 96–115

Citation in format AMSBIB
\Bibitem{Gly09}
\by S.~D.~Glyzin
\paper Difference approximations of ``reaction--diffusion'' equation on a segment
\jour Model. Anal. Inform. Sist.
\yr 2009
\vol 16
\issue 3
\pages 96--115
\mathnet{http://mi.mathnet.ru/mais67}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. D. Glyzin, “Uravnenie “reaktsiya – diffuziya” i ego konechnomernye analogi”, Trudy sedmoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (3–6 iyunya 2010 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, Samarskii gosudarstvennyi tekhnicheskii universitet, Samara, 2010, 72–75  mathnet
    2. D. S. Glyzin, S. A. Kaschenko, “Dinamika kompleksnogo prostranstvenno-raspredelennogo uravneniya Khatchinsona”, Model. i analiz inform. sistem, 19:5 (2012), 35–39  mathnet
    3. S. D. Glyzin, “Razmernostnye kharakteristiki diffuzionnogo khaosa”, Model. i analiz inform. sistem, 20:1 (2013), 30–51  mathnet
    4. S. D. Glyzin, P. L. Shokin, “Diffuzionnyi khaos v zadache «reaktsiya–diffuziya» c ganteleobraznoi oblastyu opredeleniya prostranstvennoi peremennoi”, Model. i analiz inform. sistem, 20:3 (2013), 43–57  mathnet
    5. S. A. Kaschenko, “Relaksatsionnye kolebaniya v modelyakh mnogovidovykh soobschestv”, Model. i analiz inform. sistem, 20:5 (2013), 5–24  mathnet
    6. Ya. Yu. Larina, L. I. Rodina, “Statisticheskie kharakteristiki upravlyaemykh sistem, voznikayuschie v razlichnykh modelyakh estestvoznaniya”, Model. i analiz inform. sistem, 20:5 (2013), 62–77  mathnet
    7. V. G. Bogaevskaya, I. S. Kaschenko, “Vliyanie zapazdyvayuschei obratnoi svyazi na ustoichivost periodicheskikh orbit”, Model. i analiz inform. sistem, 21:1 (2014), 53–65  mathnet
    8. S. V. Aleshin, S. A. Kaschenko, “Lokalnaya dinamika logisticheskogo uravneniya, soderzhaschego zapazdyvanie”, Model. i analiz inform. sistem, 21:1 (2014), 73–88  mathnet
    9. S. A. Kaschenko, V. E. Frolov, “Asimptotika ustanovivshikhsya rezhimov konechno-raznostnykh approksimatsii logisticheskogo uravneniya s zapazdyvaniem i s maloi diffuziei”, Model. i analiz inform. sistem, 21:1 (2014), 94–114  mathnet
    10. S. V. Aleshin, S. D. Glyzin, S. A. Kaschenko, “Uravnenie Kolmogorova–Petrovskogo–Piskunova s zapazdyvaniem”, Model. i analiz inform. sistem, 22:2 (2015), 304–321  mathnet  mathscinet  elib
    11. S. V. Aleshin, S. D. Glyzin, S. A. Kaschenko, “Osobennosti dinamiki uravneniya Kolmogorova–Petrovskogo–Piskunova s otkloneniem po prostranstvennoi peremennoi”, Model. i analiz inform. sistem, 22:5 (2015), 609–628  mathnet  crossref  mathscinet  elib
    12. E. A. Marushkina, “Ustoichivye tsikly i tory sistemy iz trekh i chetyrekh diffuzionno svyazannykh ostsillyatorov”, Model. i analiz inform. sistem, 23:6 (2016), 850–859  mathnet  crossref  mathscinet  elib
    13. S. D. Glyzin, E. A. Marushkina, “Neuporyadochennye kolebaniya v neiroseti iz trekh ostsillyatorov s zapazdyvayuschei veschatelnoi svyazyu”, Model. i analiz inform. sistem, 25:5 (2018), 572–583  mathnet  crossref
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