TY - JOUR
T1 - Crafting networks to achieve, or not achieve, chaotic states
AU - De Nigris, Sarah
AU - Leoncini, Xavier
PY - 2015/4/27
Y1 - 2015/4/27
N2 - 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 and the average eccentricity 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 thermodynamical 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 effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies with d>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.
AB - 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 and the average eccentricity 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 thermodynamical 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 effective dimension d as a crucial parameter: topologies with d<2 exhibit no phase transitions, while topologies with d>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.
UR - http://www.scopus.com/inward/record.url?scp=84929120709&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.91.042809
DO - 10.1103/PhysRevE.91.042809
M3 - Article
AN - SCOPUS:84929120709
SN - 1539-3755
VL - 91
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 042809
ER -