# System of delay differential equations: using first interpolation as second initial condition

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 with 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.