Nonseparation Approach to General-Decay Synchronization of Quaternion-Valued Neural Networks with Mixed Time Delays
Round 1
Reviewer 1 Report
- In the introduction section, the authors are discussing different types of synchronisation: “For example, finite-time synchronization [4], fixed-time synchronization [5], exponential synchronization[6], asymptotic synchronization [7].” However, important types of synchronization are missing, e.g., partial synchronisation (doi: 10.1016/S0167-2789(02)00654-1) and multi-clustering (doi: 10.1109/TAC.2020.3012528).
- Line 54: “Therefor” —> Therefore.
- After (1), there is no need to say that j is from J. The same happens after (2).
- There is a fundamental flaw in equation (3). Functions \tilde f_j cannot depend on the synchronization errors \omega_i. Such simplification can happen in case of linear activation functions f-s, but not in the truly nonlinear situation. This is actually acknowledged in lines 108 and 109. Please correct this and discuss whether it has any implications for the proofs of the main results.
- Line 115: “function is non-minus” reads rather odd. Why not to right “\geq 0”?
- Defintion 2: “(3) can be general decay stable” —> what does it mean that the system can be general decay stable? Is it general decay stable or not under the condition of Def. 2?
- Assumption 3: “\rho(t)\inC(R,R^+)” —> \rho\in C(R,R^+) since \rho(t) usually denotes the value of function \rho: R \to R^+ evaluate at point t. The same comment holds for many places of the paper in which the functions and their values are mixed. For example, again in Assumption 3, “For the functions \Psi(t)” (should be \Psi and not \Psi(t)).
Author Response
Our detailed point-to-point response with regard to the comments of Reviewers is attached in the pdf file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The referee recommends this paper for publication in Axioms, but several necessary changes need to be addressed through a Major Revision. Below are the key areas that require attention:
1. The motivation behind the study should be further emphasized. It is essential to clearly demonstrate the main advantages of the results in the paper compared to existing approaches.
2. An algorithm for implementing the proposed scheme should be included in the paper.
3. The construction of the Lyapunov-Krasovskii functional (Page 5, Line 135) must be explained in detail so that the reader can understand it well.
4. The feasibility of Assumption 3 and the condition (8) in Theorem 1 should be discussed. It is crucial to explain how users can achieve these conditions, as they are design-oriented. Providing physical meanings to support the development of the general decay synchronization is also necessary.
5. The example section needs to be expanded to include remarks that showcase the effectiveness and efficiency of the proposed method compared to other approaches.
6. For clarity, the MATLAB detail (MATLAB *.m) of Example 1 in Appendix A should be provided.
Considering and addressing these corrections is crucial for the acceptance of the manuscript. Once these revisions are made, the paper may be accepted for publication in Axioms.
English should be further improved, since the paper has some grammar errors.
Author Response
Our detailed point-to-point response with regard to the comments of Reviewers is attached in the pdf file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have partially addressed by comments raised in the previous review round. I would like to point out the following:
1. Comment 4. The way how authors define functions \tilde f_j is incorrect. These functions depend on both w_j and z_j and not on w_j only. Please see lines 108-109.
2. Comment 6. The response to comment 6 is frustrating. The question was why you use "can" in the definition(!). Rephrasing, you say that: "if condition A holds, then the system can have property B." --> Should be "If condition A holds, then the system has property B."
3. Finally, typos in references:
[10] -- authors' names and surnames are mixed up.
[12] -- "markovian" --> Markovian
Author Response
First, we would like to thank the editor and reviewers for their careful reading of this paper and helpful comments, which are very useful for improving the quality of the paper "Nonsepearion approach to general decay synchronization of quaternion-valued neural networks with mixed time delays". In consideration of the reviewers' valuable comments, we have modified the improper language expressions and technical errors. In the following, we will provide a detailed point-to-point response with regard to the comments of Reviewers.
Author Response File: Author Response.pdf
Reviewer 2 Report
It is important to ensure clarity for readers by considering and showcasing the details of MATLAB (*.m) files in Appendix A. By including relevant MATLAB codes in the appendix, it becomes easier for readers to verify and understand the presented results. Furthermore, in the article mentioned here (https://www.hindawi.com/journals/ddns/2023/2013300/), MATLAB code is provided without concerns related to patent protection.
Author Response
First, we would like to thank the editor and reviewers for their careful reading of this paper and helpful comments, which are very useful for improving the quality of the paper "Nonsepearion approach to general decay synchronization of quaternion-valued neural networks with mixed time delays". In consideration of the reviewers' valuable comments, we have modified the improper language expressions and technical errors. In the following, we will provide a detailed point-to-point response with regard to the comments of Reviewers.
Author Response File: Author Response.pdf
