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Volume 3, Issue 2
Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model

Michael Busch & Jeff Moehlis

DOI: 10.4208/nmtma.2010.32s.2

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 143-161.

Published online: 2010-03

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  • 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.

  • Keywords

Territorial behavior, Voronoi tessellations, bifurcation, center manifold reduction

  • AMS Subject Headings

37N25, 37G10

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.32s.2}, url = {http://global-sci.org/intro/article_detail/nmtma/5993.html} }
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 -

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.

Michael Busch and Jeff Moehlis. (2010). Analysis of a Class of Symmetric Equilibrium Configurations for a Territorial Model. Numerical Mathematics: Theory, Methods and Applications. 3 (2). 143-161. doi:10.4208/nmtma.2010.32s.2
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