TY - JOUR
T1 - Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model
AU - Michael Busch & Jeff Moehlis
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 143
EP - 161
PY - 2010
DA - 2010/03
SN - 3
DO - http://doi.org/10.4208/nmtma.2010.32s.2
UR - https://global-sci.org/intro/article_detail/nmtma/5993.html
KW - Territorial behavior, Voronoi tessellations, bifurcation, center manifold reduction
AB - <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>