Document Type
Article
Publication Date
2008
Publication Title
Complex Systems
Volume
17
Issue
4
First Page
357
DOI
https://doi.org/10.25088/ComplexSystems.17.4.357
Abstract
This study provides an analysis of the dynamics of fixed-size directed Boolean networks governed by generalizations of elementary cellular automata rules 22 and 126, under a power-law distribution of parent nodes and a popularity parent assignment. The analysis shows the existence of a two-piece chaotic attractor for smaller values of the power-law parameter which evolves into a "cloud"-like attractor for larger values of the parameter. Values of the parameter for which the system exhibits an ordered behavior are indicated as well. The dynamics are investigated using space-time diagrams, delay plots, bifurcation diagrams, and Lyapunov exponent computations. It is also shown that the children (out)links do not obey a power-law distribution; more precisely, numerical investigations indicate that the children links have a Gaussian-like distribution.
Recommended Citation
Goodman, Ray and Velcsov, Mihaela T., "Dynamics of Directed Boolean Networks under Generalized Elementary Cellular Automata Rules, with Power-Law Distributions and Popularity Assignment of Parent Nodes" (2008). Mathematics Faculty Publications. 81.
https://digitalcommons.unomaha.edu/mathfacpub/81
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
Complex Systems is Platinum Open Access. This means permanent and free access to published scientific works for readers with no publication fees for the authors—100% free. All articles are published under the most flexible reuse standard—the CC BY license (https://creativecommons.org/licenses/by/4.0).
This was published under Mihaela Velscov prior last name Mihaela Matache.