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
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...
, 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
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function.
The function is often thought of as an "unknown" to be solved for, similarly to ...
(as continuous infinite-dimensional systems), BDEs are intended as a (
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediat ...
) first step on the challenging road to further understanding and
modeling
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
them. For instance, one can mention complex problems in
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...
,
climate
Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologica ...
dynamics, solid-earth
geophysics
Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...
, and many problems elsewhere in
natural sciences
Natural science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and repeat ...
where much of the discourse is still
conceptual
Conceptual may refer to:
Philosophy and Humanities
*Concept
*Conceptualism
*Philosophical analysis (Conceptual analysis)
*Theoretical definition (Conceptual definition)
* Thinking about Consciousness (Conceptual dualism)
*Pragmatism (Conceptual p ...
.
One example of a BDE is the
Ring oscillator
A ring oscillator is a device composed of an odd number of NOT gates in a ring, whose output oscillates between two voltage levels, representing ''true'' and ''false''. The NOT gates, or inverters, are attached in a chain and the output of the ...
equation: , which produces periodic oscillations. More complex equations can display richer behavior, such as nonperiodic and chaotic (deterministic) behavior.
External links
*
Boolean Delay Equations: A New Type of Dynamical Systems and Its Applications to Climate and Earthquakes*
*
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References
Dynamical systems
Mathematical modeling
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