Delay differential equation

Summary

In a delay differential equation, the rate of change at time $t$ depends on the state at earlier times, such as $t - \tau$. To solve it, one must give the whole history of the solution on an initial interval, not just one initial value. So the natural state space is a space of functions, and the equation is infinite-dimensional even for one unknown. Delay equations model systems with reaction times, such as feedback control, population dynamics and epidemics.