Review Reports

Round 1

Reviewer 1 Report

I do have an objection to the diffusion models in general. However, they omit stationarity behaviour. Of course, the arithmetic results support this approach. I suggest authors to comment what' going wrong if the behaviour is not diffusive, as a  separate part.

The authors provide a deterministic optimal control approach about the impact of the technology dispersion on the sustainability of the enterprises. Their approach tests this 'optimal' behaviour with respect to stability, according to perturbation of the significant variables. The organization of the paper is poor, because the exact definition of the above notions is missing. Similar previous work references are also missing. The content of the paper is similar to an ''exercise'' either of well -known techniques of optimal control, or an exercise on the solutions of a deterministic dynamical system's differential equations. Another question is which is the relation between the content of the paper and diffusion, which involves stochastic differential equations and certain infinitesemal operations related to the heat partial differential equation. Authors should rewrite the paper having in mind all of the above remarks and the annotated ones mentioned in the pdf file of their submission. Consequently the paper needs a major revision.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Review of article axioms 2508527
Research on the Dynamic Mechanism of Technological Innova-
tion Diffusion in Enterprise Communities Based on Predation
Diffusion Model
Jingfei Chen , Gang Tian
In the paper, the authors propose to apply the mathematical model of predator-prey to the model in the economy of production and consumption. The study is proposed to be carried out using the mathematical apparatus of the qualitative theory of differential equations. Job analysis leads to the following questions:
1. The attention of the authors is drawn to the fact that the qualitative theory of differential equations is intended for the study of bifurcation points and has a local character. The dynamics of the development of the economic process for a certain period cannot be determined.
2. The authors consider a nonlinear system of differential equations (1) and (2) and use methods to study a linear system of differential equations, find bifurcation points (4). It is recommended that authors look at the theory for working with a nonlinear system.
3. The introduction does not reflect a constructive analysis of sources for solving the problem.
4. According to the text, the material is presented without comments, the example is Jacobian (5) - for which system. Then, in a general form, the characteristic equation (6), the conclusion without mathematical comments.
5. Examples of calculations with relative values are given - to characterize bifurcation points?
Conclusion. Work in this version is not of interest for the study of economic processes. Serious rework is required.
Reviewer.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

In the introduction, it is necessary to specify in more detail the purpose of the study. It is necessary to provide a research hypothesis. In addition, the research methods used in the study should be specified. With the models discussed in the article, it is necessary to specify their use conditions and strengths and weaknesses. When comparing different models, you must state which ones are better under certain conditions and why. In the summary of the research results, evaluating the proposed methods and determining their impact on the economy is necessary. It is also necessary to define the application areas of the proposed methods in the economy. More space in the conclusion should be devoted to evaluating the methods and determining their usefulness in practice.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Rereview of the materials of the article axioms 2508527
Familiarize yourself with the responses to the comments of the first round.
Unfortunately, I did not receive the necessary comments in the answers. In addition to what was noted in the first round, we can add that economic processes develop over time and the qualitative theory of differential equations is not a very suitable tool for studying these processes. The author did not pay attention to remarks with relative data for the economic process. The economy depends on many indicators with different units of measurement.
Conclusion. The article needs significant revision.
Reviewer.

Author Response

I understand the expert's advice. But in this article, we do not use differential methods to analyze long-term economic changes, but rather use differential methods as a tool to analyze whether the original equilibrium state of the enterprise community system has been broken after the intervention of "technological innovation", and how the enterprise community system will respond in a short period of time. Perhaps the expression in this article is not clear enough, and I am very sorry for this. We also hope that expert can give us an opportunity to express our opinions. Although this article may not be mature and complete, we kindly request expert to give us an opportunity to publish it. Thank you.