Pattern formation on trees.
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the nodes of a tree is described by a nonlinear map, giving rise to a coupled map lattice system. The coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination. The spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution that manifests itself in the bifurcation structure of the spatially synchronized modes. These models may describe reaction-diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure.
Cosenza
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Centro de Astrofísica Teórica, Universidad de Los Andes, Apartado Postal 26, La Hechicera, Mérida 5251, Venezuela.
Tucci
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