Questions about delayed differential equations which are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.
Delay differential equations (DDEs) or, time-delay systems differ from ordinary differential equations in that the derivative at any time depends on the solution (and in the case of neutral equations on the derivative) at prior times.
The simplest constant delay equations have the form $$y'(t) = f(t, y(t), y(t-\tau_1), y(t-\tau_2),\ldots, y(t-\tau_k))$$ where the time delays (lags) $~\tau_j~$ are positive constants. More generally, state dependent delays may depend on the solution, that is $~\tau_i = \tau_i (t,y(t)) \ .~$
Systems of delay differential equations now occupy a place of central importance in all areas of science and particularly in the biological sciences (e.g., population dynamics and epidemiology). Interest in such systems often arises when traditional point wise modeling assumptions are replaced by more realistic distributed assumptions, for example, when the birth rate of predators is affected by prior levels of predators or prey rather than by only the current levels in a predator-prey model.
References:
https://en.wikipedia.org/wiki/Delay_differential_equation
http://www.scholarpedia.org/article/Delay-differential_equations
