Variances as order parameter and complexity measure for random Boolean networks

Author(s): Luque, B; Ballesteros, FJ; Fernandez, M

Source: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL  Volume: 38   Issue: 5   Pages: 1031-1038   DOI: 10.1088/0305-4470/38/5/005   Published: FEB 4 2005

Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.