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Boolean delay equation

From Wikipedia, the free encyclopedia

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.[1]

References

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  1. ^ Cavalcante, Hugo L. D. de S.; Gauthier, Daniel J.; Socolar, Joshua E. S.; Zhang, Rui (2010). "On the origin of chaos in autonomous Boolean networks". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 368 (1911): 495–513. arXiv:0909.2269. Bibcode:2010RSPTA.368..495C. doi:10.1098/rsta.2009.0235. ISSN 1364-503X. PMID 20008414. S2CID 426841.

Further reading

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