Volume 41, Number 6, March II 1998
|Page(s)||599 - 604|
|Published online||01 September 2002|
Ordered and disordered dynamics in random networks
Department of Physiology, McGill University,
3655 Drummond Street, Montreal, Quebec, Canada H3G 1Y6
2 Department of Physics, McGill University, Montreal, Quebec, Canada
3 Department of Physics, Cornell University, Ithaca, NY, USA
Corresponding author: firstname.lastname@example.org
Accepted: 29 January 1998
Random Boolean networks that model genetic networks show transitions between ordered and disordered dynamics as a function of the number of inputs per element, K, and the probability, p, that the truth table for a given element will have a bias for being 1, in the limit as the number of elements . We analyze transitions between ordered and disordered dynamics in randomly constructed ordinary differential equation analogues of the random Boolean networks. These networks show a transition from order to chaos for finite N. Qualitative features of the dynamics in a given network can be predicted based on the computation of the mean dimension of the subspace admitting outflows during the integration of the equations.
PACS: 05.45.+b – Theory and models of chaotic systems / 05.50.+q – Lattice theory and statistics; Ising problems / 87.22.Jb – Muscle contraction, nerve conduction, synaptic transmission, memorization, and other neurophysiological processes (excluding perception processes and speech)
© EDP Sciences, 1998
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