## 3 Results
The symbols indicate the parameters used in Figure 2.  
Figure 2: Time series of the laser intensity (normalized to zero –mean and unit variance) in different locking regions: **(a)** 1:1 locking for \(f_{mod}=5\) MHz, \(a_{mod}=0.045\); **(b)** 2:1 locking for \(f_{mod}=24\) MHz, \(a_{mod}=0.0125\); **(c)** 3:1 locking for \(f_{mod}=42\) MHz, \(a_{mod}=0.0125\) (these parameters were indicated in Figure 1 with a circle, a triangle, and a square, respectively). In all panels, the red dots mark the spike times (when the intensity decreases below the threshold \(-1.1\)). To unveil the role of the modulation amplitude, we show in Figures 3 and 4 the effect of increasing \(a_{mod}\), for two modulation frequencies such that for appropriate \(a_{mod}\), the modulation produces 1:1 (Figure 3) or 2:1 (Figure 4) locked spikes. In Figure 3, we see that 1:1 locking occurs for high enough \(a_{mod}\) (panel e), while if the modulation amplitude is not too large (as in our experiments), we see that the spike timing is irregular. Note that in this figure, panel (a) displays the \"natural\", unmodulated intensity dynamics. In Figure 4 we see that regular 2:1 locking occurs for \(a_{mod}=0.0125\) [panel (b)]. The locked behavior is rigid in the sense that it persists in a range of \(a_{mod}\) values; if \(a_{mod}\) is too small, the spike timing is irregular, while if it is too large, the spikes become poorly defined. The locking region has smooth boundaries; therefore, we cannot define a precise range of \(a_{mod}\  
The locking regions are separated by regions where the spikes are unlocked. An example of the transition of 2:1 locking to 3:1 locking that occurs when the modulation frequency increases is shown in Figure 5. This transition corresponds to moving along an horizontal line in the panels displayed in Figure 1. In Figure 5 we see that for \(f_{mod}=35\) MHz (panel a) and 40 MHz (panel d), the spikes are locked (2:1 and 3:1, respectively) while for frequencies in between, there is the intermittent alternation of 2:1 and 3:1 locked spikes. This is consistent with the results shown in Figure 1c, where we see that \(\sigma_{ISI}/\left<ISI\right>\) is small in the locking regions, while it grows in the transition region. For particular values of the modulation amplitude and frequency, a spike can occur every modulation cycle. An example is shown in Figure 6a; it corresponds, in Figure 1b to the \"blue dot\" within the green area. There is no \"rigid\" locking as the regular spiking dynamics is not robust to small changes of the parameters (i.e., there is no range of frequencies or amplitudes within which the regular behavior persists). We note that the shape of the spikes in Figure 6a and in Figure 2a is different. This may be due to the fact that the modulation parameters, both amplitude and frequency, are very different: in Figure 6a, \(a_{mod}=0.012\), \(f_{mod}=16\) MHz, while in Figure 2a, \(a_{mod}=0.045\), \(f_{mod}=5\) MHz. This \"blue dot\" is visible because it is located within the green area; it is possible that other \"blue dots\" exist that are not visible because they are located within the blue area. As explained before, optical feedback introduces a set of coexisting steady-state solutions (the external cavity modes, ECMs, which can be stable modes or unstable modes). Under current modulation the ECMs turn into limit cycles that can be stable or unstable. For particular values of the modulation amplitude and frequency, after a transient, the system ends in a limit cycle and the intensity displays periodic oscillations without spikes. An example is shown in Figure 6b. When this occurs, after the transient, \(\left<ISI\right>/T_{mod}=1\) and \(\sigma_{ISI}/\left<ISI\right>\) is small. As in the case of 1:1 locked spikes, there is no \"rigidity\", i.e., we have not found parameter regions where these regular oscillations persist.