@Article{NMTMA-3-143,
author = {Michael Busch and Jeff Moehlis},
title = {Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2010},
volume = {3},
number = {2},
pages = {143--161},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2010.32s.2},
url = {http://global-sci.org/intro/article_detail/nmtma/5993.html}
}