2009/09/30 by Hugo L. D. de S. Cavalcante, Daniel J. Gauthier, Joshua E. S. Socolar +1 · 46 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Boolean function #Boolean network #CHAOS (operating system) #Class (philosophy) #Combinatorics #Computer science #Gene Regulatory Network Analysis #Ideal (ethics) #Logic gate #Mathematics #Nonlinear Dynamics and Pattern Formation #Theoretical computer science #Topology (electrical circuits) #Variety (cybernetics) #nlin.AO #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1098/rsta.2009.0235
published in Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences 368(1911), 495-513 (Royal Society) · 18 pages, 10 figures, submitted to Delayed Complex Systems International Workshop 2009
arxiv created 2009/10/15 · openalex publication_date 2009/12/14 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We undertake a systematic study of the dynamics of Boolean networks to determine the origin of chaos observed in recent experiments. Networks with nodes consisting of ideal logic gates are known to display either steady states, periodic behaviour or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power law. In an experiment, the non-ideal behaviour of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and asymmetry between the logic states tend to engender periodic behaviour, at least for the simplest networks. On the other hand, we find that a memory effect termed 'degradation' can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices may find application in a variety of technologies requiring fast complex waveforms or flat power spectra, and can be used as a test-bed for fundamental studies of real-world Boolean-like networks.