Exploring the Dynamic Organization of Random and Evolved Boolean Networks

Gianluca D’Addese,Salvatore Magrì,Roberto Serra,Marco Villani

doi:10.3390/a13110272

Abstract

The properties of most systems composed of many interacting elements are neither determined by the topology of the interaction network alone, nor by the dynamical laws in isolation. Rather, they are the outcome of the interplay between topology and dynamics. In this paper, we consider four different types of systems with critical dynamic regime and with increasingly complex dynamical organization (loosely defined as the emergent property of the interactions between topology and dynamics) and analyze them from a structural and dynamic point of view. A first noteworthy result, previously hypothesized but never quantified so far, is that the topology per se induces a notable increase in dynamic organization. A second observation is that evolution does not change dramatically the size distribution of the present dynamic groups, so it seems that it keeps track of the already present organization induced by the topology. Finally, and similarly to what happens in other applications of evolutionary algorithms, the types of dynamic changes strongly depend upon the used fitness function.

Highlights

Many natural, social or artificial systems can be described as networks of interacting elements, where the dynamical variables are associated to the nodes of the network, and directed links represent the influence of a variable upon another one
We performed knock-out experiments in 50 random Boolean networks (RBNs) each composed by 50 nodes—following an approach already developed in [12]—blocking to zero, one at a time, each node whose average activity on the attractor was greater than 0.5
“class”, and to indicate a single exponent belonging to the aforementioned class

Summary

Introduction

Social or artificial systems can be described as networks of interacting elements, where the dynamical variables are associated to the nodes of the network, and directed links represent the influence of a variable upon another one. While networks can represent different kinds of systems and relationships, let us consider here for the sake of definiteness a dynamical system. N), which can take either continuous or discrete values, is associated to every node i of the network at time t, and a deterministic law (e.g., a differential or finite difference equation) determines the time behavior of xi. If this equation contains at least one term which depends upon xj there is a link from node j to node i. The discovery of the widespread presence of some types of topological relationships, associated to important generic properties (like e.g., the presence of hubs), prompted several studies on topology [1,2,3]

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Conclusion