We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultrawide band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultrawide-band source of radio waves.
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http://dx.doi.org/10.1103/PhysRevE.80.045202 | DOI Listing |
Chaos
July 2024
Department of Mathematics, University of Castilla-La Mancha, Albacete 02071, Spain.
In this paper, we study the dynamics of synchronous Boolean networks and extend previously obtained results for binary Boolean networks to networks with state variables in a general Boolean algebra of 2p elements, with p>1. The method to do this is based on the Stone representation theorem and the relation of such systems on general Boolean algebras with those with binary-state values. Specifically, we deal with the main periodic orbit problems and predecessor problems (existence, coexistence, uniqueness, and number of them), which allows us to determine the periodic structure and the attractor cycles of the system.
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June 2024
Department of Computer Science, University of Vermont, Burlington, Vermont 05405, USA.
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems comprised of many interacting elements (often called "synergistic" information). This "emergent" organization has been found in a variety of natural and artificial systems, although at present, the field lacks a unified understanding of what the consequences of higher-order synergies and redundancies are for systems under study. Typical research treats the presence (or absence) of synergistic information as a dependent variable and report changes in the level of synergy in response to some change in the system.
View Article and Find Full Text PDFFront Comput Neurosci
August 2023
Département de Physique, Faculté des Sciences, Institut Quantique, Université de Sherbrooke, Sherbrooke, QC, Canada.
Reservoir computing provides a time and cost-efficient alternative to traditional learning methods. Critical regimes, known as the "edge of chaos," have been found to optimize computational performance in binary neural networks. However, little attention has been devoted to studying reservoir-to-reservoir variability when investigating the link between connectivity, dynamics, and performance.
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February 2023
Department of Mathematics and Mathematical Biocomplexity Division, University of Virginia, P.O. Box 400298, Charlottesville, Virginia 22904, USA.
Mathematical models rooted in network representations are becoming increasingly more common for capturing a broad range of phenomena. Boolean networks (BNs) represent a mathematical abstraction suited for establishing general theory applicable to such systems. A key thread in BN research is developing theory that connects the structure of the network and the local rules to phase space properties or so-called structure-to-function theory.
View Article and Find Full Text PDFEntropy (Basel)
January 2023
Centro de Ciencias de la Complejidad, Universidad Nacional Autonóma de México, Ciudad de México 04510, Mexico.
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional).
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