Include Delay Differential Equations Directly in Dynamic Simulations
Include Delay Differential Equations Directly in Dynamic Simulations
This shows a dynamic simulation of a differential delay logistic equation 
compared to an ordinary differential logistic equation 
.
Manipulate[
Module[{T = 50, sol, sold},
sol = First[y /. NDSolve[{y'[t] == a y[t](1 - y[t]), y[0] == 0.1}, y, {t, 0, T}]];sold = First[y /. NDSolve[{y'[t] == a y[t](1 - y[t - 1]), y[t /; t ≤ 0] == 0.1}, y, {t, 0, T}]];
ParametricPlot[{{sol[t], sol[t - 1]}, {sold[t], sold[t - 1]}}, {t, 1, T}, PlotRange -> {{0, 3}, {0, 3}}, PlotStyle -> {Gray, Blue}]], {{a, 1}, 0, 2}]