versus $t$ for $0\leq t\leq 125$. The responses to the delta functions at $t=0$ and $\tau $, as well as the echo at time $t=2\tau $ are clearly illustrated. The effect of lower $N$ is to increase the fluctuations making the echo somewhat less distinct. We do not see any echo at $t=3\tau $. This is in agreement with Eq. (40), since $h_3=0$ for the $h(\theta )$ employed in these computations. Figure 3 shows a blow-up of the numerically computed echo around the time $t=2\tau $ for $N=10^6$, $10^5$, and $10^4$. Also, plotted in Fig. 3 as asterisks is the result from our theoretical calculation Eq. (39). Reasonable agreement between the theoretical and computed echo shapes is obtained, although the agreement is somewhat obscured by fluctuation effects at the smaller system sizes $(N)$. While our choice $\hat d_0=\hat
d_1=1/4$ might be regarded as questionable for applicability of the small amplitude approximation $(\hat d_p\ll 1$, for $p=0,1$) employed by Eq. (7) and by our theory of Sec. III, we have nonetheless evidently obtained good agreement between the theory and numerical experiment. Figure 4 illustrates the effect of varying the driving amplitude for a network of size $N=10^4$. For $\hat d_0=\hat d_1=1/8$ 