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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 203, Number 1, Pages 10–25
DOI: https://doi.org/10.4213/tmf9824 (Mi tmf9824) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Diffusion chaos and its invariant numerical characteristics

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

a Demidov Yaroslavl State University, Yaroslavl, Russia
b Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (775 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf9824
Abstract: For distributed evolutionary dynamical systems of the "reaction–diffusion" and "reaction–diffusion–advec-tion" types, we analyze the behavior of invariant numerical characteristics of the attractor as the diffusion coefficients decrease. We consider the phenomenon of multimode diffusion chaos, one of whose signatures is an increase in the Lyapunov dimensions of the attractor. For several examples, we perform broad numerical experiments illustrating this phenomenon.
Keywords: reaction–diffusion system, diffusion chaos, attractor, Lyapunov dimension.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10055
This research was supported by the Russian Foundation for Basic Research (Grant No. 18-29-10055).
Received: 18.09.2019
Revised: 29.11.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 203, Issue 1, Pages 443–456
DOI: https://doi.org/10.1134/S0040577920040029
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Diffusion chaos and its invariant numerical characteristics”, TMF, 203:1 (2020), 10–25; Theoret. and Math. Phys., 203:1 (2020), 443–456
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v203/i1/p10
    • This publication is cited in the following 3 articles:
    1. L. I. Ivanovskiy, “Dynamical properties of a diffusion-coupled system of differential equations with an additional internal coupling”, Theoret. and Math. Phys., 220:2 (2024), 1282–1293  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. L. I. Ivanovskii, “Dinamika odnoi sistemy diffuzionno svyazannykh differentsialnykh uravnenii s dopolnitelnoi vnutrennei svyazyu”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2020, no. 3, 15–30  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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