Boolean dynamics of networks with scalefree topology
Abstract
The dynamics of Boolean networks with scalefree topology are studied. The existence of a phase transition from ordered to chaotic dynamics, governed by the value of the scalefree exponent of the network, is shown analytically by analyzing the overlap between two distinct trajectories. The phase diagram shows that the phase transition occurs for values of the scalefree exponent in the open interval (2, 2.5). Since the Boolean networks under study are directed graphs, the scalefree topology of the input connections and that of the output connections are studied separately. Ultimately these two topologies are shown to be equivalent. A numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scalefree topologies and networks with homogeneous random topologies. However, an important result of this work is that the finetuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scalefree. Finally, based on the results presented in this work, it is hypothesized that the scalefree topology favors the evolution and adaptation of network functioning from a biological perspective.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 October 2003
 DOI:
 10.1016/S01672789(03)00174X
 Bibcode:
 2003PhyD..185...45A
 Keywords:

 05.45.+b;
 87.10.+e;
 64.60.Cn;
 64.60.Ht;
 General theory and mathematical aspects;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Dynamic critical phenomena