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Incoming links: Exact polynomial steps for a delay equation
Delay differential equation Created 2026-10-06 Updated 2026-10-18
A delay differential equation relates a derivative at the current argument to values at earlier arguments. For example, the Buchstab function obeys for .
The defining feature is memory: a derivative can depend on earlier values of the unknown function. Constant delays, time-dependent delays, and delays depending on the unknown function belong to this wider class. The retarded delay differential equation below isolates a single positive constant delay.[ref]
Delay-differential equations by Skip Thompson. Skip Thompson, Delay-differential equations, opening definition and equation (1): constant and state-dependent delays
The Malthusian delay differential equation is a simple linear member of this class. The method of steps for a delay differential equation constructs its future from a history function of a delay differential equation, and the characteristic equation of a delay differential equation studies its exponential function modes. The exact polynomial steps for a delay equation below make that construction explicit without approximating the solution of a differential equation. Applications include population dynamics and feedback control; the delayed negative feedback model and feedback delay explain why the timing of a return matters as well as its sign.