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Pattern Formation on Trees

M. G. Cosenza·K. Tucci
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Abstract

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, given 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 which manifest 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.

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M. G. Cosenza, K. Tucci. 2001-05-04. Pattern Formation on Trees. https://doi.org/10.1103/physreve.64.026208

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