Ordered and disordered dynamics in random networks

¹ 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: glass@cnd.mcgill.ca

Received: 20 October 1997
Accepted: 29 January 1998

Abstract

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.