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Matem. Mod., 1997, Volume 9, Number 12, Pages 43–56 (Mi mm1486)  

This article is cited in 8 scientific papers (total in 8 papers)

Mathematical models and computer experiment

Population models with non-linear diffusion

N. V. Belotelova, A. I. Lobanovb

a The Centre on the Problems of Ecology and Productivity of Forests
b Moscow Institute of Physics and Technology

Abstract: Population reaction-diffusion models with nonlinear diffusion are considered. Two classes of the models are investigated – the models of one population and the models of competing populations. In the first class several types of kinetics are considered. The dynamics of the population outbreak is studied for different kinetics. Outbreak spreading front has finite supporter in every time for each case. This phenomenon principally differs from Kolmogorov's waves. In the second class of the models the possibility of appearing stationary spatially nonhomogeneuos solutions is analyzed. Amplification of the Gause principle for spatially distributed competing systems is formulated.

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Received: 29.04.1997

Citation: N. V. Belotelov, A. I. Lobanov, “Population models with non-linear diffusion”, Matem. Mod., 9:12 (1997), 43–56

Citation in format AMSBIB
\Bibitem{BelLob97}
\by N.~V.~Belotelov, A.~I.~Lobanov
\paper Population models with non-linear diffusion
\jour Matem. Mod.
\yr 1997
\vol 9
\issue 12
\pages 43--56
\mathnet{http://mi.mathnet.ru/mm1486}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1609633}
\zmath{https://zbmath.org/?q=an:0993.92501}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. A. Volosov, “A Property of the Ansatz of Hirota's Method for Quasilinear Parabolic Equations”, Math. Notes, 71:3 (2002), 339–354  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. V. Shmidt, “Analysis of reaction-diffusion systems by the method of linear determining equations”, Comput. Math. Math. Phys., 47:2 (2007), 249–261  mathnet  crossref  mathscinet  zmath  elib  elib
    3. Usenko V.A., Lobanov A.I., “Metod potokovoi relaksatsii dlya resheniya kvazilineinykh uravnenii parabolicheskogo tipa”, Kompyuternye issledovaniya i modelirovanie, 3:1 (2011), 47–53  elib
    4. Budyanskii A.V., Tsibulin V.G., “Modelirovanie prostranstvenno-vremennoi migratsii blizkorodstvennykh populyatsii”, Kompyuternye issledovaniya i modelirovanie, 3:4 (2011), 477–488  elib
    5. V. A. Usenko, A. I. Lobanov, “Metod potokovoi relaksatsii dlya resheniya kvazilineinykh uravnenii parabolicheskogo tipa”, Kompyuternye issledovaniya i modelirovanie, 3:1 (2011), 47–53  mathnet  crossref
    6. A. V. Budyanskii, V. G. Tsibulin, “Modelirovanie prostranstvenno-vremennoi migratsii blizkorodstvennykh populyatsii”, Kompyuternye issledovaniya i modelirovanie, 3:4 (2011), 477–488  mathnet  crossref
    7. L. E. Alpeeva, V. G. Tsibulin, “Kosimmetrichnyi podkhod k analizu formirovaniya prostranstvennykh populyatsionnykh struktur s uchetom taksisa”, Kompyuternye issledovaniya i modelirovanie, 8:4 (2016), 661–671  mathnet  crossref
    8. A. V. Epifanov, V. G. Tsibulin, “O dinamike kosimmetrichnykh sistem khischnikov i zhertv”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 799–813  mathnet  crossref
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