Parallel Simulation of Adaptive Random Boolean Networks

Kirill Kuvshinov , Klavdiya Bochenina , Piotr Górski , Janusz Hołyst

Abstract

A random Boolean network (RBN) is a generic model of interactions between entities with binary states that has applications in different fields. As real-world systems often operate on the border between order and chaos, algorithms simulating RBN's transition to a critical state are of particular interest. Adaptive RBNs (ARBNs) can evolve towards such a state by rewiring of nodes according to their states on the attractor. Numerical simulation of ARBNs larger than several dozens of nodes is computationally hard due to an enormous growth of attractor lengths and transient periods. In this paper, we propose a GPGPU algorithm for parallel simulation of ARBNs with modified activity-dependent rewiring rule which can be used with any sequential algorithm for attractor's search. In the experimental part of the study, we investigate the performance of parallel implementation and the influence of parameters of the algorithm on the speed of convergence to a steady state.