I am trying to solve numerically the following system of two coupled delay differential equations:

$ $ \dot x(t)=-\gamma x(t)-\frac{\gamma}{4}e^{i\omega_0\tau_1}y(t-\tau_1)\theta(t-\tau_1)+\frac{\gamma}{4}e^{i\omega_0\tau_2}y(t-\tau_2)\theta(t-\tau_2)+\frac{\gamma}{2}e^{i\omega_0\tau_3}x(t-\tau_3)\theta(t-\tau_3),$ $ $ $ \dot y(t)= -\frac{\gamma}{2}y(t)-\frac{\gamma}{4}e^{i\omega_0\tau_1}x(t-\tau_1)\theta(t-\tau_1)+\frac{\gamma}{4}e^{i\omega_0\tau_2}x(t-\tau_2)\theta(t-\tau_2).$ $ where $ \tau_1<\tau_2<\tau_3$ . The parameters $ \gamma, \omega_0$ are constants, and $ \theta(t)$ is the Heaviside step function. The history of the system is known for $ 0\leq t\leq\tau_1$ : $ $ x(t)=e^{-\gamma t}, y(t)=e^{-\gamma t/2}.$ $ **Here what I tried:**

I first solved the system for $ 0\leq t\leq\tau_2$ using the aforementioned initial history using NDSolve:

`\[Gamma] = 1.0; \[Omega]0 = 2 Pi; \[Tau]1 = 1.0; \[Tau]2 = 2.0; \[Tau]3 = 3.0; sol1 = NDSolve[{x'[ t] == - \[Gamma] x[t] - (\[Gamma]/4) E^(I \[Tau]1 \[Omega]0) y[t - \[Tau]1], y'[t] == - 0.5 \[Gamma] y[t] - (\[Gamma]/4) E^( I \[Tau]1 \[Omega]0) x[t - \[Tau]1], x[t /; t <= \[Tau]1] == (1.0/Sqrt[2.0]) Exp[-\[Gamma] t], y[t /; t <= \[Tau]1] == (1.0/Sqrt[2.0]) Exp[-0.5 \[Gamma] t]}, {x, y}, {t, 0, \[Tau]2}]; `

I get the following solution for $ |x(t)|^2$ and $ |y(t)|^2$ :

The problem arises when I use this first interpolated solution as the initial history to solve for the next interval of time:

`sol2 = NDSolve[{x'[ t] == - \[Gamma] x[t] - (\[Gamma]/4) E^(I \[Tau]1 \[Omega]0) y[t - \[Tau]1] + (\[Gamma]/4) E^(I \[Tau]2 \[Omega]0) y[t - \[Tau]2], y'[t] == - 0.5 \[Gamma] y[t] - (\[Gamma]/4) E^( I \[Tau]1 \[Omega]0) x[t - \[Tau]1] + (\[Gamma]/4) E^( I \[Tau]2 \[Omega]0) x[t - \[Tau]2], x[t /; t <= \[Tau]2] == Evaluate[x[t] /. sol1], y[t /; t <= \[Tau]2] == Evaluate[y[t] /. sol1]}, {x, y}, {t, 0, \[Tau]3}]; `

This time I get the following messages:

It seems that the second NDSolve (sol2) does not allow the interpolation of the first result as initial history. Any suggestion? Thank you in advance.