Bulletin of Mathematical Biology

, Volume 68, Issue 2, pp 451–466

Density-dependent migration and synchronism in metapopulations

Original Article

DOI: 10.1007/s11538-005-9054-8

Cite this article as:
Silva, J.A.L. & Giordani, F.T. Bull. Math. Biol. (2006) 68: 451. doi:10.1007/s11538-005-9054-8


A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.



Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Departamento de Matemática Pura e Aplicada-IM-UFRGSPorto Alegre-RS, BrasilBrazil