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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 3, Pages 622–635 (Mi smj1201)  
This article is cited in 3 scientific papers (total in 3 papers)

Local and global properties of nonautonomous dynamical systems and their application to competition models

V. G. Il'ichev

Rostov State University
Full-text PDF (226 kB) Citations (3)
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Abstract: We develop the inheritance principle for local properties by the global Poincare mapping of nonautonomous dynamical systems. Namely, if a semigroup property is uniformly locally universal then it is enjoyed by the global Poincare mapping. In studying the global dynamics of competitors in a periodic medium, the crucial role is played by the multiplicative semigroup of the so-called sign-invariant matrices. We give geometric criteria for stability of equilibria (periodic solutions) in competition models.
Keywords: universality, semigroup, coarseness, sign-invariant matrices, competition, global stability.
Received: 24.04.2001
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 3, Pages 490–499
DOI: https://doi.org/10.1023/A:1023816915603
Bibliographic databases:
UDC: 517.711.2:577.4
Language: Russian
Citation: V. G. Il'ichev, “Local and global properties of nonautonomous dynamical systems and their application to competition models”, Sibirsk. Mat. Zh., 44:3 (2003), 622–635; Siberian Math. J., 44:3 (2003), 490–499
Citation in format AMSBIB
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\vol 44
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\pages 622--635
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\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 3
\pages 490--499
\crossref{https://doi.org/10.1023/A:1023816915603}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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