Stability of Boolean Multilevel Networks

Abstract

The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks in multiplex (multi-layered) graphs. Our main finding is that the multilevel structure provides a mechanism for the stabilization of the dynamics of the whole system even when individual layers work on the chaotic regime, therefore identifying new ways of feedback between the structure and the dynamics of these systems. Our results point out the need for a conceptual transition from the physics of single layered networks to the physics of multiplex networks. Finally, the fact that the coupling modifies the phase diagram and the critical conditions of the isolated layers suggests that interdependency can be used as a control mechanism.

Final version. It includes the generalization to the case of having an arbitrary number of layers

References in corpus (7)

• Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
• The Yeast Cell-Cycle Network Is Robustly Designed
• Topological Evolution of Dynamical Networks: Global Criticality from Local Dynamics
• Topology of biological networks and reliability of information processing
• Correlated multiplexity and connectivity of multiplex random networks
• Stable and unstable attractors in Boolean networks
• The effect of network topology on the stability of discrete state models of genetic control

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