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Updated: Jul 25, 2026

Design, Surface Treatment, Cellular Plating, and Culturing of Modular Neuronal Networks Composed of Functionally Inter-connected Circuits
Published on: April 15, 2015
Crafting networks to achieve, or not achieve, chaotic states
Sarah De Nigris1, Xavier Leoncini2
1Department of Mathematics and Namur Center for Complex Systems-naXys, University of Namur, 8 rempart de la Vierge 5000 Namur, Belgium.
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.
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