Boolean delay equation

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.

Hopes and promises

Although in recent centuries, differential equations (both ordinary and partial) have extensively served as quantitative models of vast categories of problems, by the recent greedy and rapid burst of complexities everywhere, the gap between quantitative and qualitative modeling and reasoning techniques is widening. BDEs offer a formal mathematical language that is promising to help bridge that gap.

External links

• Ghil M, Zaliapin I. "A Novel Fractal Way: Boolean Delay Equations and Their Applications to the Geosciences" (PDF). atmos.ucla.edu. {{cite journal}}: Cite journal requires |journal= (help)
• Boolean Delay Equations: A New Type of Dynamical Systems and Its Applications to Climate and Earthquakes
• Wright DG, Stocker TF, Mysak LA (1990). "A note on quaternary climate modelling using Boolean delay equations" (PDF). Climate Dynamics. 4 (4): 263–7. doi:10.1007/BF00211063.{{cite journal}}: CS1 maint: multiple names: authors list (link)
• Oktem H, Pearson R, Egiazarian K (2003). "An adjustable aperiodic model class of genomic interactions using continuous time Boolean networks (Boolean delay equations)". Chaos. 13 (4): 1167–74. doi:10.1063/1.1608671. PMID 14604408. {{cite journal}}: Unknown parameter |month= ignored (help)CS1 maint: multiple names: authors list (link)
• Ghil M, Zaliapin I, Coluzzi B (2008). "Boolean Delay Equations: A simple way of looking at complex systems". Physica D. 237: 2967–86. doi:10.1016/j.physd.2008.07.006. arXiv:nlin.CG/0612047.{{cite journal}}: CS1 maint: multiple names: authors list (link)