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Peer-Review Record

Hidden Dynamics and Hybrid Synchronization of Fractional-Order Memristive Systems

Axioms 2022, 11(11), 645;
by Haipeng Jiang 1, Lizhou Zhuang 1, Cheng Chen 2 and Zuolei Wang 1,*
Reviewer 1: Anonymous
Reviewer 3:
Axioms 2022, 11(11), 645;
Submission received: 21 September 2022 / Revised: 29 October 2022 / Accepted: 10 November 2022 / Published: 15 November 2022
(This article belongs to the Special Issue Fractional-Order Equations and Optimization Models in Engineering)

Round 1

Reviewer 1 Report

Please see the “Review of the paper” file.

Comments for author File: Comments.pdf

Author Response

Responses: Thanks for your comments and suggestions, with which our manuscript was improved. We read the manuscript carefully and revised it point by point according to your comments.


Point 1. The manuscript proposes the system (4) as a "new" system of fractional-order, but it is unclear how it is new. That is, is it so new that there are no results at all showing similar results in the study of fractional-order memristive systems, or not? It is necessary to properly assert the degree of novelty by clarifying the significance and positioning of this study along with the history of research a little more in the Introduction section.


Response 1. Thank you for your comments. How system (4) is new is explained in our revised manuscript. The history of memeristor system is depicted in the Introduction section.


Point 2. The dynamical analysis of the new system in this paper is insufficient. I suggest the authors should combine Lyapunov exponents spectrum, offset boosting analysis and spectral entropy complexity analysis to make further discussions.


Response 2. Thanks for your suggestions. To further verify the results in our paper, corresponding Lyapunov exponents are calculated and given our revised paper. Further discussions about the proposed system, such as offset boosting analysis and spectral entropy complexity analysis, will be carried out in our another work.


Point 3. Can the newly proposed system be implemented in the circuit? If possible, I suggest the authors add a section to discuss the simulations of the coexistence of different attractors by a corresponding analog electronic circuit to verify the realizability of the new system.


Response 3. Thanks for your suggestions. The newly proposed system can be implemented in the circuit. To verify the realizability of the new system, the simulations of the coexistence of different attractors by a corresponding analog electronic circuit will be studied in our another work mainly involving dynamics analysis.

Author Response File: Author Response.docx

Reviewer 2 Report

The work "Hidden dynamics and hybrid synchronization of fractional-order memristive systems", by Haipeng Jiang, Llzhou Zhuang, Cheng Chen, and Zuolei Wang, deals a fractional-order system with an included memristive component. That such system has not equilibrium points and present attractors. Moreover, the hybrid synchronization problem with the master-salve scheme is also boarded, where the stability of the error system is proved with stability theory for fractional order systems. The work is interesting with the popular fractional-order approach.

In the authors sense, in the absence of equilibria every emerging attractor could be considered as hidden. However, there are a lot of work with the particular case of emerging chaotic behavior without equilibria, and the creators do not call it hidden.

I suggest the authors must to mention the version of hiddens and multistability in terms of the basin attraction and unstable equilibria. For this approach, authors can take a view on the following references and references there in: 

1. A two-directional grid multiscroll hidden attractor based on piecewise linear system and its application in pseudo-random bit generator, Integration, Vol. 81, pp. 34-42,

2. Chapter 3: Generation of Self-excited and Hidden Multiscroll Attractors in Multistable Systems, Recent Trends in Chaotic, Nonlinear and Complex Dynamics, pp. 40-78 (2021).

3. Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems, in Complexity, Dynamics, Control, and Applications of Nonlinear Systems with Multistability, Vol. 2020.

Moreover, it is dessirable that authors to explain the difference between both of these approaches.

The consider that this work can be improved and publishable with this proposed discussion about hiddens.


Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

In the present paper, the authors study fractional-order memristive system without equilibrium. They explain hidden attractors of the proposed system and coexistence of hidden attractor is found. The hybrid synchronization of proposed system with partial controllers investigates through theoretical analysis. Further, numerical simulation verifies the validity of the hybrid synchronization scheme.

The theme of paper is good but this paper needs minor improvements. The following are comments and suggestions:


·         Page 4 and Page 6, Bifurcation Diagrams: Make more clear figures.

·        Page 9, Equation (13): Explain little calculations, how to get equation (13)?


Page 2, line 34: “Synchronization” should be “synchronization”.

Page 2, line 42: “follows” should be “follows:”.

Page 7, line 132: “And” should be “and”.

Page 8, Equation (11): At the end of equation “,” should be “.”.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The revised paper can be accepted.

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