Crafting networks to achieve, or not achieve, chaotic states

الأصل · EN

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 d2 exhibit no phase transitions while ones with d2 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.