# Talk:Desynchronization (computational neuroscience)

The authors presented a concise review of various methods of desycnrhonization of neuronal populations. I have few suggestions for improvements.

1. It seems that equations numbering is lost in the text. Also in many instances references to equations are missing. Please check.

2. Please provide definition of “vulnerable phase”. 3. Figure 2. What “p” on the vertical axis means? Please specify. 4. It is not clear from the text what are advantages of nonlinear delayed feedback compared to linear delay feedback method. Please clarify. 5. Is there experimental evidence that methods reviewed in the paper actually work? References to experimental work will be useful. Also, references to works where these methods were applied to biophysically plausible models (rather than simple phase oscillators) will be useful as well.

## Responses:

We thank the Referee for his/her suggestions which improved the article.

1. We have carefully checked the text with respect to the numbering of the equations and the references to them.

2. We give the definition of the “vulnerable phase” when we first time mentioned it in Sec. 2 “Single-pulse stimulation”:

"The vulnerable phase denotes the critical value of the mean phase \(\Psi_{cr}(t)\) of synchronized ensemble at which the population is most capable to exhibit stimulation-induced desynchronization (Tass 1999, see also Winfree 1977)."

3. We specified the meaning of the quantity “p” when discussing Fig.2 in Sec.2:

"A single pulse of appropriate strength delivered at a vulnerable phase of a fully synchronized population of phase oscillators desynchronizes the population both in the absence (Winfree 1980) and in the presence (Tass 1999) of noise, see Fig. 2 where the time course of the firing density \(p(t)\), the average number density of the oscillators which have zero phase at time \(t\) is shown."

4. We briefly mentioned the advantages of the nonlinear delayed feedback as compared to the linear delayed feedback in Sec.7:

"The above properties, namely, the robustness with respect to parameter variation (compare Fig. 11 to Fig. 9), the precise control of the extent of synchronization, and the frequency control distinguish the NDF desynchronizing method from the linear single-site delayed feedback. Another peculiarity of NDF is an indirect control of synchronization as discussed below."

5. The considered Kuramoto system is a simple and well-known model for collective phase dynamics which is an object of the control of the presented methods and is used for illustrative purposes to explain the mechanisms of control. Of course, the discussed methods have been tested on many very different models of different complexity. Some of them, such as single-pulse stimulation, coordinated reset stimulation, linear single-site delayed feedback, and nonlinear delayed feedback have also been verified experimentally. For the interested reader we include the bibliography for further reading at the end of the sections, where additional papers are cited, which investigate the desynchronizing methods for other models. We also included a few additional citations, where experimental results are reported. We write at the end of Sec. 1 when introducing the Kuramoto model:

"The efficacy and the main properties of several desynchronization methods will be illustrated below on exemplary phase ensemble (1). However, the discussed methods have successfully been applied to more complicated and realistic models including neuronal ensembles. Some of them have been tested experimentally as well, see the bibliography for further reading at the end of the corresponding sections."