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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 5, Pages 860–875 (Mi zvmmf4876)  

This article is cited in 18 scientific papers (total in 18 papers)

Finite-dimensional models of diffusion chaos

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a Faculty of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000 Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992 Russia

Abstract: Some parabolic systems of the reaction-diffusion type exhibit the phenomenon of diffusion chaos. Specifically, when the diffusivities decrease proportionally, while the other parameters of a system remain fixed, the system exhibits a chaotic attractor whose dimension increases indefinitely. Various finite-dimensional models of diffusion chaos are considered that represent chains of coupled ordinary differential equations and similar chains of discrete mappings. A numerical analysis suggests that these chains with suitably chosen parameters exhibit chaotic attractors of arbitrarily high dimensions.

Key words: reaction-diffusion system, diffusion chaos, attractor, Lyapunov dimension, chain of coupled mappings.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:5, 816–830

Bibliographic databases:

UDC: 519.624.2
Received: 10.12.2009

Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Finite-dimensional models of diffusion chaos”, Zh. Vychisl. Mat. Mat. Fiz., 50:5 (2010), 860–875; Comput. Math. Math. Phys., 50:5 (2010), 816–830

Citation in format AMSBIB
\by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Finite-dimensional models of diffusion chaos
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 5
\pages 860--875
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 5
\pages 816--830

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    This publication is cited in the following articles:
    1. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Relaxation oscillations and diffusion chaos in the Belousov reaction”, Comput. Math. Math. Phys., 51:8 (2011), 1307–1324  mathnet  crossref  mathscinet  isi
    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, 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
    6. 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
    7. 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
    8. A. V. Kazarnikov, S. V. Revina, “Vozniknovenie avtokolebanii v sisteme Releya s diffuziei”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:2 (2016), 16–28  mathnet  crossref  elib
    9. 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
    10. Aleshin S.V., Glyzin S.D., Kaschenko S.A., “Dynamic properties of the Fisher–Kolmogorov–Petrovskii–Piscounov equation with the deviation of the spatial variable”, Autom. Control Comp. Sci., 50:7 (2016), 603–616  crossref  isi  scopus
    11. Glyzin S.D., Shokin P.L., “Diffusion chaos in the reaction?diffusion boundary problem in the dumbbell domain”, Autom. Control Comp. Sci., 50:7 (2016), 625–635  crossref  isi  scopus
    12. Aleshin S.V., Glyzin S.D., Kaschenko S.A., “Spatially inhomogeneous structures in the solution of Fisher-Kolmogorov equation with delay”, International Conference on Computer Simulation in Physics and Beyond 2015, Journal of Physics Conference Series, 681, IOP Publishing Ltd, 2016, 012023  crossref  isi  scopus
    13. Aleshin S., Glyzin S., Kaschenko S., “Waves interaction in the Fisher?Kolmogorov equation with arguments deviation”, Lobachevskii J. Math., 38:1 (2017), 24–29  crossref  mathscinet  zmath  isi  scopus
    14. Glyzin S.D. Kolesov A.Yu. Rozov N.Kh., “Traveling-Wave Solutions in Continuous Chains of Unidirectionally Coupled Oscillators”, Vi International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012015  crossref  mathscinet  isi  scopus
    15. Glyzin S., Goryunov V., Kolesov A., “Spatially Inhomogeneous Modes of Logistic Differential Equation With Delay and Small Diffusion in a Flat Area”, Lobachevskii J. Math., 38:5, SI (2017), 898–905  crossref  mathscinet  zmath  isi  scopus
    16. V. E. Goryunov, “Bifurkatsiya Andronova–Khopfa v odnoi biofizicheskoi modeli reaktsii Belousova”, Model. i analiz inform. sistem, 25:1 (2018), 63–70  mathnet  crossref  elib
    17. Glyzin S.D. Goryunov V.E. Kolesov A.Yu., Computer Simulations in Physics and Beyond (Csp2017), Journal of Physics Conference Series, 955, IOP Publishing Ltd, 2018  crossref  isi  scopus
    18. Goryunov V.E., “The Andronov-Hopf Bifurcation in a Biophysical Model of the Belousov Reaction”, Autom. Control Comp. Sci., 52:7 (2018), 694–699  crossref  mathscinet  isi  scopus
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