TY - JOUR T1 - Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model 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 -

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.