The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions
, Atefeh Ahmadi 1, Fatemeh Bakouie 2, Amir Homayoun Jafari 3,4, Sajad Jafari 1,5 and Dibakar Ghosh 6,*Round 1
Reviewer 1 Report
The review is attached
Comments for author File: 
Comments.docx
Author Response
We thank the editor and reviewers for their insightful comments. The reviewer’s concerns have been addressed in green color, and the paper was amended consequently, as indicated below.
----------------------
Reviewer #1
Comment-1: In a classical model of Network there are only pairwise connections (links). However, in real-world networks there are also essential connections of higher order. The paper is devoted to the networks with higher order connections that are reflected by so-called simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational costs. To confound this issue, map-based models are more suitable since they are faster, simpler, more flexible, and computationally more optimal. Therefore, this paper addresses the impact of pairwise and non-pairwise neuronal interactions on the synchronization state of 10 coupled memristive Hindmarsh-Rose neuron maps. To this aim, electrical, inner linking, and chemical synaptic functions are considered as 2- and 3-body interactions in three homogenous and two non-homogenous cases. The results show that through chemical pairwise and non-pairwise synapses, the neurons achieve synchrony with the weakest coupling strengths.
The text is quite monotonous because the same analytical pattern is applied to different cases. However, the mathematical technique using Lyapunov stability theory is correct, the graphical illustrations are clear and useful, and the results have a theoretical interest from the point of view of the network theory and a practical importance.
Thus, I recommend the paper for publication in Mathematics.
Response-1: We warmly thank the reviewer for recommending our manuscript for publication.
----------------------
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Please see the attachment.
Comments for author File: Comments.pdf
Please see the attachment.
Author Response
Please see the attached response file.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The revision is well and so I suggest to accept this paper.
