
Publications [#248334] of Joshua Socolar
Papers Published
 Cavalcante, HLDDS; Gauthier, DJ; Socolar, JES; Zhang, R, On the origin of chaos in autonomous Boolean networks.,
Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, vol. 368 no. 1911
(January, 2010),
pp. 495513, ISSN 1364503X [20008414], [doi]
(last updated on 2019/06/19)
Abstract: 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 logictransition events circulating in the network per unit time grows as a power law. In an experiment, the nonideal behaviour of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain nonideal features of real logic gates that enable chaos in experimental networks. We find that shortpulse 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 Booleanlike 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 testbed for fundamental studies of realworld Booleanlike networks.
