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Matem. Mod., 2000, Volume 12, Number 1, Pages 78–93 (Mi mm831)  

This article is cited in 1 scientific paper (total in 1 paper)

Computational methods and algorithms

olynomial models of populations with autotaxis: “travelling wave” solutions

F. S. Berezovskaya, G. P. Karev

The Centre on the Problems of Ecology and Productivity of Forests

Abstract: The conceptual model of a population with attractant being a system of a “reaction-diffusion-crossdiffusion” type is considered. The analysis of “travelling wave” solutions of a model with polynomial functions of population growth (Malthus, logistics, Alle type) and polynomial intensity of autotaxis is carried out in a neighbourhood of local equilibria by methods of bifurcation theory. The different spatially non-homogeneous wave regimes (wave-fronts, impulses, trains etc.) are described, an evolution of travelling wave characteristics with increase of degrees of growth and taxis polynomial functions, variation of model parameters and velocity of spread was analysed sequentially. The possibilities of application of obtained results under research of a phenomenon of pattern density formation in the spatially distributed populations (such as plancton communities and phytofage populations) are discussed. The founded non-monotone wave regimes could be interpreted as moving spatially non-homogeneous distributions (patches) of population density.

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Received: 14.01.1999

Citation: F. S. Berezovskaya, G. P. Karev, “olynomial models of populations with autotaxis: “travelling wave” solutions”, Matem. Mod., 12:1 (2000), 78–93

Citation in format AMSBIB
\Bibitem{BerKar00}
\by F.~S.~Berezovskaya, G.~P.~Karev
\paper olynomial models of populations with autotaxis: ``travelling wave'' solutions
\jour Matem. Mod.
\yr 2000
\vol 12
\issue 1
\pages 78--93
\mathnet{http://mi.mathnet.ru/mm831}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1773207}
\zmath{https://zbmath.org/?q=an:1027.92508}


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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. Horstmann, D, “A constructive approach to traveling waves in chemotaxis”, Journal of Nonlinear Science, 14:1 (2004), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus
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