Thanks for addressing most of the reviewers' comments. After a second round, clarifications can still be made on the method and the type of forcing used. Please see the detailed comments of the reviewer.

Dear Authors,
Thank you for submitting the revised version of your manuscript. I appreciate your dedication to improving the work, which I continue to believe is worthy of publication.
At this stage, however, it appears that some disagreements between the reviewer and the authors remain unresolved. To avoid a prolonged cycle of revisions where positions remain unchanged, I recommend preparing a detailed response to the reviewer’s comments. Additionally, for the critical points, I would like to provide my recommendations below to help finalize the manuscript:
1. Model Description: Including a few concise sentences summarizing each part of the model would greatly enhance clarity. While it is acceptable to reference other papers for additional details, please ensure the description here is self-contained and sufficient for understanding, without unnecessary detail.
2. Figure 3: The clarity and correctness of this manuscript should take precedence over maintaining consistency with any previous work. I concur with the reviewer that further improvements are needed for Figure 3. Please ensure the reviewer’s recommendations are addressed comprehensively.
3. Definition of Operator H: I agree with the reviewer’s observation that the current formulation of Equation 3 is problematic. I recommend defining the operator H to depend explicitly on two arguments: N(X,θ) and X(t). For greater generality, you may consider allowing H to depend on a function N and the variable X(t).
I believe these revisions will strengthen your paper and resolve any outstanding issues. Please don’t hesitate to reach out if you need further clarification.

All the comments have been successfully addressed