Boolean delay equation

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.

External links

• A Novel Fractal Way: Boolean Delay Equations and Their Applications to the Geosciences. atmos.ucla.edu. http://www.atmos.ucla.edu/tcd/PREPRINTS/BDE_rev05_B.pdf. Retrieved 2006-05-26. 
• Boolean Delay Equations: A New Type of Dynamical Systems and Its Applications to Climate and Earthquakes
• "A note on quaternary climate modelling using Boolean delay equations". Climate Dynamics 4 (4): 263–7. 1990. doi:10.1007/BF00211063. Bibcode: 1990ClDy....4..263W. 
• "An adjustable aperiodic model class of genomic interactions using continuous time Boolean networks (Boolean delay equations)". Chaos 13 (4): 1167–74. December 2003. doi:10.1063/1.1608671. PMID 14604408. Bibcode: 2003Chaos..13.1167O. http://link.aip.org/link/?cha/13/1167&agg=MEDLINE_CHA. 
• "Boolean Delay Equations: A simple way of looking at complex systems". Physica D 237 (23): 2967–86. 2008. doi:10.1016/j.physd.2008.07.006. Bibcode: 2008PhyD..237.2967G.