A New 4D Hyperchaotic System and Its Analog and Digital Implementation

Round 1

Reviewer 1 Report

This work introduces a 4D hyper-chaotic system, and its electronic implementation both in analog and discrete versions.

The text is clear and easy to understand. However, it is not clear for which problem the paper proposes a solution, the novelty of the paper is not clearly stated. A comparison, highlighting the superiorities of the proposed 4D system and advantages of its digital implementation, can enhance the content of the paper. There already exist several number of 4D systems, similarly with 2 quadratic nonlinearities (e.g., see modified 4D Lorenz or Liu or 4D Lü systems etc).  Discrete implementations of chaotic systems always sound suspicious since they are theoretically duplicable due to limited numerical resolution, which is not preferred for security applications. The application to benefit the proposed digital implementation should be mentioned.

There exist minor grammar issues in the text.

 

Proof of Theorem 1: It is not clear why (6) has to be always satisfied. Actually, (6) is another way of writing V_dot<0, which guarantees trajectories to be bounded if and only if this condition is satisfied. There is also no explanation regarding the sign of the coefficients. If the value of c is sufficiently large, (2) would indicate non-dissipation. These points should be made clear by the authors.

Figure 1: range of parameter d is given as [1.5-5] instead of [0.5-5]. Figure captions (c,d) are giving wrong information as well.

Lyapunov Exp.: There exist positive Lyapunov exp. for d = [0.5-5]? Is the system in the chaotic regime then? This does not agree with Fig. 1.

KY dimension: The formula given in (9) assumes j=3 but j is replaced by 2, regarding the first appearance of it (j+…).

Figure 3: axis information of (c) and (f) are wrong.

Figure 5: axis information (e.g. amplitude values) are missing.

Electronic Implementation: replacing w with (-w) in (11) would simplify the electronic implementation of in Fig.4, i.e. tow inverting amplifiers corresponding to x and w variables should be unnecessary. A similar approach should be considered for the optimization of the digital implementation as well.

Table 3 and Table 4 can be merged into a single table to enable a quick comparison between them.

Line 80: NCS should be NHS.

Line 132: Section title is wrong.

Line 172: check the grammar please.

Line 174: change Fig 6 to Fig 4.

Line 178-9: Fig 5 and Fig 6 demonstrate implementation results rather than the implementations.

 

 

Author Response

Dear Reviewer ,

Thank you very much for your comments, which were very useful to enrich our  work, and therefore, the comments provided improve the manuscript its quality which helped us a lot to realize our mistakes and how we could improve it.

Please check the report attached where you can see the question for each question. In addition we added a cover letter. 

Best Regards

Cesar Cruz. 

Author Response File: Author Response.pdf

Reviewer 2 Report

 The author presented a new four-dimensional autonomous hyperchaotic system based on Méndez-Arellano-Cruz-Martínez (MACM) 3D chaotic system. Analytical and numerical studies of the dynamic properties were conducted to generate hyperchaos for the new hyperchaotic system (NHS) in its continuous version (CV) calculating the Lyapunov exponents. The CV of the NHS was simulated and implemented using operational amplifiers (OAs), and the algorithm of the Discretized Version (DV) of NHS was simulated and implemented in real-time.  I have the following reviews:

The authors should add a contribution section to the introduction.

The literature review should be extended as it lacks in depth analysis of proposed techniques.

 

Author Response

Dear Reviewer,

Thank you very much for your comments, which were very useful to enrich our  work, and therefore, the comments provided improve the manuscript its quality which helped us a lot to realize our mistakes and how we could improve it.

Please check the report attached where you can see the question for each question. In addition we added a cover letter. 

Best Regards

Cesar Cruz. 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I would like to thank to the authors since the technical quality of the paper, after the revision, is definitely improved.

Please replace “hiperchaotic” (in the title and the in rest of the text) with “hyperchaotic”!

Please correct equation (9): replace (2+…) with (3+…)! The result is correct but the equation is still wrong.

Equation (11) is not visible in the revised manuscript but I assume that it is correct.

I would like to suggest the authors to review the English of the text. There exist grammar mistakes at more than one place.

Author Response

Dear Reviewer, 

Thanks so much for your 2nd comments. We appreciate so much your guide line to improve the second version of the proposed work. 

Please check attached the answer for your comments. 

Best Regards, 

Cesar Cruz

Author Response File: Author Response.pdf