American Institute of Mathematical Sciences

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2008, 5(4): 843-857. doi: 10.3934/mbe.2008.5.843

Density-dependent dispersal in multiple species metapopulations

Jacques A. L. Silva 1, and  Flávia T. Giordani 1,

1. 

Depto. de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul, Av. Bento Gon¸calves, 9500. Bairro Agronomia, Porto Alegre, RS, Brazil, Brazil

Received  December 2007 Revised  May 2008 Published  October 2008

A multiple species metapopulations model with density-dependent dispersal is presented. Assuming the network configuration matrix to be diagonizable we obtain a decoupling of the associated perturbed system from the homogeneous state. It was possible to analyze in detail the instability induced by the density-dependent dispersal in two classes of $k$-species interaction models: a hierarchically organized competitive system and an age-structured model.
Keywords: multiple species, density-dependent migration, metapopulation.
Mathematics Subject Classification: Primary: 92B05; Secondary: 93C55, 93C10.
Citation: Jacques A. L. Silva, Flávia T. Giordani. Density-dependent dispersal in multiple species metapopulations. Mathematical Biosciences & Engineering, 2008, 5 (4) : 843-857. doi: 10.3934/mbe.2008.5.843
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