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.
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