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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 9, Pages 54–68 (Mi ivm9279)  

This article is cited in 3 scientific papers (total in 3 papers)

Investigation of solutions to one family of mathematical models of living systems

N. V. Pertseva, B. Yu. Pichugina, A. N. Pichuginab

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 13 Pevtsova str., Omsk, 644043 Russia
b Omsk State University, 55A Mira Ave., Omsk, 644077 Russia
Full-text PDF (243 kB) Citations (3)
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Abstract: We consider a family of integral equations used as models of some living systems. We establish a reduction of the integral equation to the equivalent Cauchy problem for a non-autonomous differential equation with a point or distributed delay dependent on a choice of a elements survival function. We also investigate questions of existence, uniqueness, nonnegativity and extendibility of solutions. We describe all stationary solutions and obtain sufficient conditions of their asymptotic stability. We have found sufficient conditions of existence of a limit of solutions on infinity and present an example of a research of equations in which the production speed of elements of living systems is described by means of unimodal function (Hill function).
Keywords: nonlinear integral equation of convolution type, differential equation with delay, differential equation with distributed delay, asymptotic stability of solutions of nonlinear integral equation, limit of solutions of nonlinear integral equation, mathematical model of living system, survival function, unimodal function, Hill function.
Received: 26.04.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 9, Pages 48–60
DOI: https://doi.org/10.3103/S1066369X17090067
Bibliographic databases:
Document Type: Article
UDC: 517.929 : 57
Language: Russian
Citation: N. V. Pertsev, B. Yu. Pichugin, A. N. Pichugina, “Investigation of solutions to one family of mathematical models of living systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 9, 54–68; Russian Math. (Iz. VUZ), 61:9 (2017), 48–60
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/ivm/y2017/i9/p54
  • 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
    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Abstract page:154
    Full-text PDF :42
    References:44
    First page:9
     
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