Dynamical Investigation of a Modified Cubic Map with a Discrete Memristor Using Microcontrollers

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors explored the application of memristors in addressing the challenges associated with investigating oscillations in dynamic and chaotic systems. They employed two types of microcontrollers to assess the performance of these systems. This study holds promise for enhancing the efficiency of dynamic systems. However, several issues warrant consideration, as outlined below:

In abstract:

(1) Clearly emphasize the key findings of the study, particularly the main challenges currently faced in the research area.

(2) The novelty of the study should be made more explicit.

(3) Highlight the research outcomes in comparison to existing works in the field.

In introduction:

(4) I recommend highlighting the weaknesses and shortcomings of the analyzed works that necessitated this study. Please, present these points in bullet format for clarity.

(5) Please, clearly outline the main contributions of the case studies to emphasize their significance.

In mathematical model:

(6) Provide a detailed description of all variables and parameters in the existing equations, including M(q) and any other relevant cases that were previously omitted.

In numerical results:

(7) It is essential to provide a more thorough exploration of the reported results and observations, as the authors currently only present charts without in-depth analysis.

(8) I recommend including comparative results that demonstrate the efficiency of the proposed idea in cubic maps relative to other existing solutions.

In implementation with microcontrollers:

 

(9) The reported results require additional analysis to provide deeper insights into their implications and significance.

Comments for author File: Comments.pdf

Author Response

Dear reviewer 1,

Thank you for your helpful comments. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this article, a new discrete map is proposed, which is generated by coupling a cubic map with a discrete memristor. Its dynamical behaviour is then investigated and the proposed map is validated by numerical analysis with two microcontrollers. Overall, the selection of topics for this article has some merit, but there are several issues that need to be addressed before publication.

1.      The studies related to discrete memristive map cited in the introduction section of the article are relatively outdated, and it is recommended that the authors discuss and cite more recent and relevant studies in the introductory section. For example: Nonlinear Dynamics, 2024, Early Access, https://doi.org/1007/s11071-024-10513-1; Analysis of the dynamical behavior of discrete memristor-coupled scale-free neural networks, Chinese Journal of Physics, 2024, Pages 966-976.

2.      The article did not analyze the characteristics of the proposed memristor model, such as hysteresis loops. It is suggested that the author add relevant content.

3.      To make it easier for the reader to understand the creative inspiration, the author can explain the choice of Cubic map over other maps as the coupling map.

4.      It is true that there exists a hyperchaotic interval for the cubic map with integrated discrete amnesia presented in the text, but the interval is rather short and the value of the second largest Lyapunov exponent is small. In this case, the authors do not make a good case for the superiority of the discrete model mentioned in the introductory part of the text. It is recommended that the authors optimise the proposed model or the relevant parameters to solve this problem.

5.      How to prove that the chaotic attractors in Figure 5 (c) and Figure 7 (b) (c) (d) are hyperchaotic? Add corresponding LE for explanation.

6.      It is recommended that authors add a vision for future research work to help other researchers expand on the research presented.

Author Response

Dear Reviewer 2,

Thank you for your helpful comments. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Major Revisions

The manuscript presents a dynamical investigation of a modified cubic map incorporating a discrete memristor, implemented using two microcontrollers (PIC32MZ2048EFH144 and STM32H723ZG). While the study has potential, addressing the following weaknesses would significantly enhance its impact and effectiveness:

1. The novelty of the Approach: Although the combination of the cubic map and discrete memristor is presented, the techniques used are relatively standard in nonlinear dynamics. The novelty seems limited to the specific combination and its microcontroller implementation. Highlighting unique contributions and contextualizing them within existing literature is essential.

2. Stability Analysis: The stability analysis is confined to fixed-point analysis. Including a more comprehensive theoretical analysis, such as bifurcation theory, could add depth and rigor to the manuscript.

3. Related Literature: Several studies are addressing cubic map systems with discrete memristors. The manuscript should differentiate itself by identifying what gap it addresses and how it advances the field.

Minor Revisions

Abstract
To make the abstract more compelling and informative, ensure it includes:

• Theoretical and practical significance of the problem.
• The methodology used to address the challenges.
• Advantages of the proposed approach.
• Details about the test system.
• Simulation results and comparisons with existing methods.

Additionally, avoid using unidentified terms (e.g., PIC32MZ2048EFH144 and STM32H723ZG) in the abstract.

Introduction

• Update the literature review to include studies from 2023 and 2024, providing a more recent and relevant context.

Conclusion

• Discuss the advantages and limitations of the proposed method.
• Summarize the challenges investigated, their importance, and the solutions provided.
• Propose improvements to address the method's limitations.
• Clearly outline the future direction of the research.

References

• Ensure references follow the journal's format. Review recent articles in the journal for guidance.
• Maintain consistent formatting for author names, article titles, journal names, and publication years.
• Avoid citation clusters. Distribute references evenly across sentences rather than grouping them in a single citation.
• Use standardized journal abbreviations (refer to resources such as CAS Source Index).

Figures, Diagrams, and Flowcharts

• Ensure consistency in color, font, and formatting across all visual elements.
• Label the horizontal and vertical axes of all graphs (e.g., Figures 9–13 currently lack axis labels).

Plagiarism

The article’s similarity index is approximately 29%, which is above the acceptable threshold of 15%. Address the following to reduce plagiarism:

• Rewrite repetitive sentences using different expressions or additional details.
• Summarize and paraphrase content from cited articles rather than directly copying text.
• Avoid directly reusing text from the authors' previous publications.

By addressing these issues, the manuscript will be significantly improved and better suited for publication in Electronics.

Author Response

Dear Reviewer 3,

Thank you for your helpful comments. Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Some addressed concerns have been resolved through the revisions provided.

Reviewer 2 Report

Comments and Suggestions for Authors

The revised paper has addressed the questions, and can be accepted.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors answered almost all the questions, and now I suggest accepting the manuscript for the journal.