Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-12-15
Physics
Condensed Matter
Disordered Systems and Neural Networks
5 pages, 4 figures
Scientific paper
Spin models of neural networks and genetic networks are considered elegant as they are accessible to statistical mechanics tools for spin glasses and magnetic systems. However, the conventional choice of variables in spin systems may cause problems in some models when parameter choices are unrealistic from the biological perspective. Obviously, this may limit the role of a model as a template model for biological systems. Perhaps less obviously, also ensembles of random networks are affected and may exhibit different critical properties. We here consider a prototypical network model that is biologically plausible in its local mechanisms. We study a discrete dynamical network with two characteristic properties: Nodes with binary states 0 and 1, and a modified threshold function with $\Theta_0(0)=0$. We explore the critical properties of random networks of such nodes and find a critical connectivity $K_c=2.0$ with activity vanishing at the critical point.
Bornholdt Stefan
Rybarsch Matthias
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