Boolean delay equation

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Boolean Delay Equations (BDEs) describe how the state of a system that can be only 0 or 1 changes over time. They are a type of semi-discrete dynamical system: the variables are Boolean-valued, but time flows continuously and the current state depends on past states after certain delays. BDEs are used as a simple, heuristic way to study complex phenomena that are hard to model with traditional continuous equations, such as problems in fluid dynamics, climate dynamics, and geophysics. A basic example is the Ring oscillator: X(t-τ) = X(t), which produces regular cycles. More complex BDEs can show richer behavior, including nonperiodic and deterministic chaotic dynamics.