Boolean delay equation explained

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:, which produces periodic oscillations. More complex equations can display richer behavior, such as nonperiodic and chaotic (deterministic) behavior.^[1]

Further reading

• Wright DG, Stocker TF, Mysak LA. A note on quaternary climate modelling using Boolean delay equations . Climate Dynamics . 4 . 4 . 263–7 . 1990 . 10.1007/BF00211063 . 1990ClDy....4..263W . 128603325 .
• Oktem H, Pearson R, Egiazarian K. An adjustable aperiodic model class of genomic interactions using continuous time Boolean networks (Boolean delay equations) . Chaos . 13 . 4 . 1167–74 . December 2003 . 14604408 . 10.1063/1.1608671 . https://archive.today/20130223112728/http://link.aip.org/link/?cha/13/1167&agg=MEDLINE_CHA . dead . 2013-02-23 . 2003Chaos..13.1167O .
• 10.1016/j.physd.2008.07.006 . Ghil M, Zaliapin I, Coluzzi B. Boolean Delay Equations: A simple way of looking at complex systems . Physica D . 237 . 2967–86 . 2008 . nlin.CG/0612047 . 23 . 2008PhyD..237.2967G . 12652082 .

Notes and References

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