Boolean delay equation (original) (raw)
A Boolean Delay Equation (BDE) is an evolution rule for the state of dynamical variables whose values may be represented by a finite discrete numbers os states, such as 0 and 1. As a novel type of semi-discrete dynamical systems, Boolean delay equations (BDEs) are models with Boolean-valued variables that evolve in continuous time. Since at the present time, most phenomena are too complex to be modeled by partial differential equations (as continuous infinite-dimensional systems), BDEs are intended as a (heuristic) first step on the challenging road to further understanding and modeling them. For instance, one can mention complex problems in fluid dynamics, climate dynamics, solid-earth geophysics, and many problems elsewhere in natural sciences where much of the discourse is still concept
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| dbo:abstract | A Boolean Delay Equation (BDE) is an evolution rule for the state of dynamical variables whose values may be represented by a finite discrete numbers os states, such as 0 and 1. As a novel type of semi-discrete dynamical systems, Boolean delay equations (BDEs) are models with Boolean-valued variables that evolve in continuous time. Since at the present time, most phenomena are too complex to be modeled by partial differential equations (as continuous infinite-dimensional systems), BDEs are intended as a (heuristic) first step on the challenging road to further understanding and modeling them. For instance, one can mention complex problems in fluid dynamics, climate dynamics, solid-earth geophysics, and many problems elsewhere in natural sciences where much of the discourse is still conceptual. One example of a BDE is the Ring oscillator equation: X(t-τ) = X(t), which produces periodic oscillations. More complex equations can display richer behavior, such as nonperiodic and chaotic (deterministic) behavior. (en) |
| dbo:wikiPageExternalLink | http://www.atmos.ucla.edu/tcd/PREPRINTS/BDE_rev05_B.pdf http://link.aip.org/link/%3Fcha/13/1167&agg=MEDLINE_CHA https://archive.today/20130223112728/http:/link.aip.org/link/%3Fcha/13/1167&agg=MEDLINE_CHA https://web.archive.org/web/20060721101338/http:/www.atmos.ucla.edu/tcd/PREPRINTS/BDE_rev05_B.pdf https://web.archive.org/web/20070928044825/http:/cdsagenda5.ictp.trieste.it/askArchive.php%3Fcateg=a0385&id=a0385s29t12&ifd=14357&down=1&type=lecture_notes |
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| rdfs:comment | A Boolean Delay Equation (BDE) is an evolution rule for the state of dynamical variables whose values may be represented by a finite discrete numbers os states, such as 0 and 1. As a novel type of semi-discrete dynamical systems, Boolean delay equations (BDEs) are models with Boolean-valued variables that evolve in continuous time. Since at the present time, most phenomena are too complex to be modeled by partial differential equations (as continuous infinite-dimensional systems), BDEs are intended as a (heuristic) first step on the challenging road to further understanding and modeling them. For instance, one can mention complex problems in fluid dynamics, climate dynamics, solid-earth geophysics, and many problems elsewhere in natural sciences where much of the discourse is still concept (en) |
| rdfs:label | Boolean delay equation (en) |
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