Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral properties and pattern selection in fractal growth networks   A model for the generation of fractal growth networks in Euclidean spaces of
arbitrary dimension is presented. These networks are considered as the spatial
support of reaction-diffusion and pattern formation processes. The local
dynamics at the nodes of a fractal growth network is given by a nonlinear map,
giving raise to a coupled map system. The coupling is described by a matrix
whose eigenvectors constitute a basis on which spatial patterns on fractal
growth networks can be expressed by linear combination. The spectrum of
eigenvalues the coupling matrix exhibits a nonuniform distribution that is
reflected in the presence of gaps or niches in the boundaries of stability of
the synchronized states on the space of parameters of the system. These gaps
allow for the selection of specific spatial patterns by appropriately varying
the parameters of the system.

29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th