Synchronization, Control and Data Assimilation of the Lorenz System

Round 1

Reviewer 1 Report

The paper entitled 'Synchronization, control and data assimilation of the Lorenz system' concerns master-slave synchronization. The authors extended the original Pecora-Carrol synchronization scheme, to partial and intermittent coupling and used metaheuristic algorithms in order to retrieve unkown parameters. I find the paper interesting, however:

1. Section 6 is not described in the introduction.

2. I believe that the paper contains too many sections and the theoretical part (e.g. sections 2-6) can be combined into one or two sections with subsections.

3. In line 264 you wrote 'For a number of repetitions M...'. What does repetitions mean? Are these actual repetitions of the algorithm execution or maybe iterations (based on the pseudocode, I believe these are iterations)? I think this information should be given precisely.

4. There are nondeterministic elements in Algorithm 2, therefore all calculations should be repeated a minimum of 10 times (preferably 30), each time using a different seed of the pseudo-random number generator, and the results should be given as the mean value and standard deviation. There is a lack of detailed information on the methodology clearly indicating the number of repetitions and computer parameters.

5. I believe that it is worth supporting the obtained results with statistical tests.

Author Response

> 1. Section 6 is not described in the introduction.

done

> 2. I believe that the paper contains too many sections and the theoretical
> part (e.g. sections 2-6) can be combined into one or two sections with
> subsections.

we have reorganised the sections according with suggestioins.

> 3. In line 264 you wrote 'For a number of repetitions M...'. What does
> repetitions mean? Are these actual repetitions of the algorithm execution
> or maybe iterations (based on the pseudocode, I believe these are
> iterations)? I think this information should be given precisely.

we have reformulated the whole session, trying to clarify the meaning of M and hoow time-series are constructed

> 4. There are nondeterministic elements in Algorithm 2, therefore all
> calculations should be repeated a minimum of 10 times (preferably 30),
> each time using a different seed of the pseudo-random number
> generator, and the results should be given as the mean value and
> standard deviation. There is a lack of detailed information on the
> methodology clearly indicating the number of repetitions and computer > parameters.

> 5. I believe that it is worth supporting the obtained results with statistical
> tests.

we reported statistical measurements in Table 3, comparing them with the ensemble statistics of Table 2

 

Reviewer 2 Report

In this manuscript, authors did not discuss implementations of the chaotic system, as mentioned in the abstract: The idea is that of having a computer replica (slave) of a natural 2 system (master, simulated in this paper), and exploit the fact that slave synchronizes with the master 3 only if they evolve with the same parameters... In the synchronization cases, authors did not compare all the cases mentioned from the method introduced by pecora and Carroll, to the proposed one given in section 8. Pruned-enriching approach. Authors must compare all the cited synchronization methods or other wise, what is the motivation of describing them?. It is obvious that one can find other recent works that can be more robust applying algorithms, as the currently published with DOI: https://doi.org/10.3390/e25030495, where the oscillators are more complex having hidden attractors.

Authors may also mention implementations of the Lorenz system and similar chaotic systems using integrated circuits CMOS, microcontrollers, raspberry Pi, FPAA or even FPGA. This can be discussed in order to show that almost all theoretical work can be implemented with electronic devices to develop engineering applications.

Author Response

> In this manuscript, authors did not discuss implementations of the
> chaotic system, as mentioned in the abstract: The idea is that of having a > computer replica (slave) of a natural 2 system (master, simulated in this
> paper), and exploit the fact that slave synchronizes with the master 3
> only if they evolve with the same parameters...

We have not fully understood the remark. We specified that we always used the Euler integration scheme. 

> In the synchronization cases, authors did not compare all the cases
> mentioned from the method introduced by pecora and Carroll, to the
> proposed one given in section 8.

We added in the conclusions that we aere planning to apply our method to other systems, like those cited by Pecora and Carrol. 

> Pruned-enriching approach. Authors must compare all the cited
> synchronization methods or other wise, what is the motivation of
> describing them?.

We do not fully understand the remark. The pruned-enriching method is used when the other ones are not applicable. 

> It is obvious that one can find other recent works that can be more
> robust applying algorithms, as the currently published with
> DOI: https://doi.org/10.3390/e25030495, where the oscillators are more > complex having hidden attractors.

We added a paragraph in the Introduction about hidden attractors and our choice of using the Lorenz system. 

> Authors may also mention implementations of the Lorenz system and
> similar chaotic systems using integrated circuits CMOS, microcontrollers,
> raspberry Pi, FPAA or even FPGA. This can be discussed in order to show
> that almost all theoretical work can be implemented with electronic
> devices to develop engineering applications.

We are actually planning to follow this suggestion. We mentioned it in the conclusions. 

Round 2

Reviewer 1 Report

The authors took into account my comments, therefore I recommend accepting the paper.

Reviewer 2 Report

The updated manusript is fine to be accepted now