Adomian Decomposition, Firing Change Process Analysis and Synchronous Control of Fractional-Order Hindmarsh–Rose Neurons in Electromagnetic Field

Round 1

Reviewer 1 Report

What is the fundamental approach of the paper, involving the construction of a fractional-order model based on integer-order Hindmash-Rose (HR) Neurons Under Electric Field?

How is the decomposition of the nonlinear term achieved in the constructed fractional-order model, and what role does the Adomian decomposition method play in obtaining the numerical solution of the system?

Could you elaborate on the comprehensive analysis conducted on the firing behavior of the neuron model, particularly through the utilization of phase diagrams, Inter Spike Interval (ISI) bifurcation diagrams, SE complexity, and the Largest Lyapunov exponent (LLE)?

How does the paper apply sliding mode control theory to design chaos synchronization controllers for the system, and what specific aspects of chaos synchronization are targeted by this approach?

In what manner are the designed chaos synchronization controllers validated, and what insights do the Matlab simulation results offer regarding the feasibility, effectiveness, and response characteristics of the controllers?

How do the findings of this research contribute to the broader understanding of memristor neural network systems, particularly in the context of control and application?

Can the developed methodologies and insights be extended or adapted to other similar neural network systems or complex nonlinear systems with practical implications?

What are the potential implications or practical applications of the fast response and effectiveness demonstrated by the chaos synchronization controller in real-world scenarios involving memristor neural networks?

Modify introduction with the help of these references

Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique

Probing Families of Optical Soliton Solutions in Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model with Improved Versions of Extended Direct Algebraic Method

 

Efficient computational approaches for fractional-order Degasperis-Procesi and Camassa–Holm equations

 

Moderate editing of English language required

Author Response

see file

Author Response File: Author Response.pdf

Reviewer 2 Report

Minor Revisions

*) In the text there are some typos that should be removed.

*) The abstract reports only qualitative results. Please provide some detail on the most significant quantitative results.

*) Some symbols are not defined in the text. Please, fill this gap.

*) For each non original mathematical formula, at least one relevant reference should be associated.

*) Please, specify how from (14) You get (15).

 

Major Revisions

*) In the Introduction it is not so clear how the contribution of the paper is necessary for developing of the research line. Please, if possible, fill this gap.

*) How the exponent (25) was obtained? Its formulation is not clear.

*) Why you exploited DC stimulus? Which kind of electromagnetic problem do you consider?

*) Physically, what do Theorems 1 and 2 mean? Please, specify.

*) The conclusions appear too poor. Please, if possible, include details not presents in other sections. Moreover, it is should be presented a short depscription of the future perspectives of the ongoing research.

Author Response

see file

Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Authors,

The report is attached to this submission.

Best wishes

Comments for author File: Comments.pdf

Moderate editing of English language required

Author Response

Thank you very much. You marked the manuscript in great detail. We have revised it according to your marking, and also revised the abstract and conclusion. The three papers you provided have been reflected in the manuscript.

Reviewer 4 Report

A new method based on the adomian decomposed algorithm applied to the control and firing of  fractional-order Hindmash-Rose neurons  is proposed.

The introductory section needs to be organized in a more structured way. The authors should briefly highlight the performance limitations of current control and firing systems of fractional-order H-R neurons and how the proposed research intends to overcome them, specifying the main research goals.

Formulas need to be reviewed carefully. There are several anomalies that confuse their reading. For example, in formula (1) the constant G is shown in bold, and is therefore interpreted as a vector; however, in line 82 hex is shown in normal font instead. The same is true for bk. Again in formula (1) N appears both in the first equation described as "a nonlinear part of the system", and in the third formula, which can be interpreted as a set of natural numbers. It is not stated on which interval of natural numbers the index j varies in (4). Furthermore, in the first equation of (1) an asterisk appears which it is not clear what it means, and in formulas (5,6) Ai is shown in bold, in vector form, but it is not stated whether it is the vector with components Aij.

A schematization of the proposed method is missing. It is necessary to facilitate the reading of sections 3 and 4. I suggest adding, in this regard, an architectural scheme or a flow diagram that includes the processes used and their connections.

The discussion of the simulation results shown in Figures 8 and 9 is too meager and needs to be explored further.

It is necessary to include future research perspectives in the concluding section.

The manuscript contains several grammatical typos that need to be corrected (for example, "In this paper" repeated twice at the beginning of the Abstract).

Author Response

see file

Author Response File: Author Response.pdf

Reviewer 5 Report

Please find attached the review report.

Comments for author File: Comments.pdf

Author Response

According to the review comments, the corresponding amendments were made.

Round 2

Reviewer 1 Report

My last two comments is add in paper.

Author Response

Relevant references have been added.

Reviewer 2 Report

All my suggestions have been implemented. Therefore, in my opinion, the paper deserves publication.

Author Response

thanks 

Reviewer 4 Report

The authors have taken into account all my suggestions and have responded comprehensively to my comments. I consider this paper publishable in the present form.

The grammar typos present in the previous version of the manuscript have been corrected.

Author Response

thanks