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Matematicheskie Zametki, 2011, Volume 90, Issue 6, Pages 860–874
DOI: https://doi.org/10.4213/mzm8578 (Mi mzm8578) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Inheritance Principle in Dynamical Systems

V. G. Ilichev

Southern Research Center of the Russian Academy of Sciences
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DOI: https://doi.org/10.4213/mzm8578
Abstract: We suggest an “inheritance principle” according to which local properties are inherited by the global shift mapping. The principle is based on the notions of roughness and semigroup. When analyzing general competition models, key inherited properties (sign-invariant structures etc.) are determined. This approach is used to prove the global stability of periodic modes in a number of nonlinear nonautonomous ecological models.
Keywords: roughness, inheritance, stability, global shift mapping, Poincaré period map, dynamics of interaction of n competitors, Hadamard's lemma, sign-invariant structure, dynamics of ecological communities.
Received: 04.06.2009
Revised: 07.12.2010
English version:
Mathematical Notes, 2011, Volume 90, Issue 6, Pages 838–849
DOI: https://doi.org/10.1134/S000143461111023X
Bibliographic databases:
Document Type: Article
UDC: 517.711.2:577.4
Language: Russian
Citation: V. G. Ilichev, “Inheritance Principle in Dynamical Systems”, Mat. Zametki, 90:6 (2011), 860–874; Math. Notes, 90:6 (2011), 838–849
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    1. Vitaly G. Il'ichev, Dmitry B. Rokhlin, “Paradoxes of Competition in Periodic Environments: Delta Functions in Ecological Models”, Mathematics, 12:1 (2023), 125  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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