$K$ between the oscillators is increased through a critical coupling strength $K_c$, there is a transition to sustained global cooperative behavior. In this state $(K>K_c)$ a suitable average over the oscillator population (this average is often called the ‘order parameter’) exhibits steady macroscopic oscillatory behavior. For $K<K_c$ a stimulus may transiently induce macroscopic oscillations, but the amplitude of these coherent oscillations (i.e., the magnitude of the order parameter) decays exponentially to zero with increasing time[@acebron05]. In the present paper we consider the Kuramoto model in the parameter range $K<K_c$, and we demonstrate that ‘echo’ phenomena occur for this system. The basic echo phenomenon can be described as follows: A first stimulus is applied at time $t=0$, and the response to it dies away; next, a second stimulus is applied at a later time, $t=\tau $, and its response likewise dies away; then at time $t=2\tau $ (also possibly at $n\tau $, for $n=3,4,\ldots$) an echo response spontaneously builds up and then decays away. An illustrative example is shown in Fig. 1, which was obtained by

![Illustration of the echo phenomenon. Stimuli at times $t=0$ and $t=\tau $ lead to direct system responses which rapidly decay away followed by echo responses 