Year: 2010
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 2 : pp. 143–161
Abstract
Motivated by an animal territoriality model, we consider a centroidal Voronoi tessellation algorithm from a dynamical systems perspective. In doing so, we discuss the stability of an aligned equilibrium configuration for a rectangular domain that exhibits interesting symmetry properties. We also demonstrate the procedure for performing a center manifold reduction on the system to extract a set of coordinates which capture the long term dynamics when the system is close to a bifurcation. Bifurcations of the system restricted to the center manifold are then classified and compared to numerical results. Although we analyze a specific set-up, these methods can in principle be applied to any bifurcation point of any equilibrium for any domain.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2010.32s.2
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 2 : pp. 143–161
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Territorial behavior Voronoi tessellations bifurcation center manifold reduction