title: Crafting networks to achieve, or not achieve, chaotic states.
abstract: 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.
authors.affiliation: Department of Mathematics and Namur Center for Complex Systems-naXys, University of Namur, 8 rempart de la Vierge 5000 Namur, Belgium.
authors.forename: Sarah
authors.initials: S
authors.lastname: De Nigris
authors.affiliation: Aix Marseille Université, Université de Toulon, CNRS, CPT UMR 7332, 13288 Marseille, France.
authors.forename: Xavier
authors.initials: X
authors.lastname: Leoncini
mesh_terms: D008962:Models, Theoretical; D056004:Molecular Dynamics Simulation; D017711:Nonlinear Dynamics; D013816:Thermodynamics