Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crafting networks to achieve, or not achieve, chaotic states   The influence of networks topology on collective properties of dynamical
systems defined upon it is studied in the thermodynamic limit. A network model
construction scheme is proposed where the number of links, the average
eccentricity and the clustering coefficient are controlled. This is done by
rewiring links of a regular one dimensional chain according to a probability
$p$ within a specific range $r$, that can depend on the number of vertices $N$.
We compute the thermodynamic behavior of a system defined on the network, the
$XY-$rotors model, and monitor how it is affected by the topological changes.
We identify the network dimension $d$ as a crucial parameter: topologies with
$d\textless{}2$ exhibit no phase transitions while ones with $d\textgreater{}2$
display a second order phase transition. Topologies with $d=2$ exhibit states
characterized by infinite susceptibility and macroscopic chaotic/turbulent
dynamical behavior. These features are also captured by $d$ in the finite size
context.

18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc