Linear Delay Differential Equations

Linear delay differential equations describe systems where the current rate of change depends not only on the current state but also on past states. Essentially, they involve equations where the derivative at a specific time is influenced by the system's values at earlier moments. This accounts for delays or memory effects in processes such as population dynamics, engineering, or economics. Unlike regular differential equations, they incorporate "delays," making the future evolution depend on the system’s history, providing a realistic way to model situations where effects don't happen instantly but take some time to manifest.