## 4 Conclusions  
For two chaotic systems of arbitrary natures that are close to each other in a reasonable sense, it is possible to achieve generalized synchronization. According to Conjecture 1, the synchronization error tends to vanish if the system difference becomes negligible. Once the driven system is equipped with the parameter estimation controller, one can fit  
Figure 14: Dependence of the error attractor \(L_{1}\)-volume on the parameter \(\mu\) value for slave systems without and with a controller on \(\hat{\mu}\), corresponding to slave systems (12) and (21), respectively.  
Figure 15: (**a**) Resistance \(R_{1}\) identification results; (**b**) Evaluation of relative error in \(R_{1}\) identification: the plot shows the actual \(R_{1}\) value versus the relative error of its estimation \(|\frac{\Delta R_{1}}{R_{1}}|\), where \(\Delta R_{1}=\hat{R_{1}}-R_{1}\).  
uncertain parameters of the driving system even though there is no straight correspondence between the systems.  
To experimentally verify Conjecture 1, we developed a novel design of a circuit modeling a Rossler chaotic system. Generalized synchronization between the circuit and computer models was established, and the synchronization error was estimated.  
Several first and second-order integration methods were tested. We experimentally confirmed that the methods of a higher-accuracy order can improve the synchronization accuracy in computer simulations. The best result was obtained by [PERSON]'s method. It is of interest that the symplectic Euler-Cromer method gave almost similar results to [PERSON]'s method, with first-order accuracy and increased computationally efficiency.  
We show that the use of adaptive generalized synchronization allows the parameters of an analog system to be tracked. We implemented a controller monitoring the parameter vector and found that the median value of one uncertain parameter fitted by this controller corresponds to the analog value with high accuracy. This opens the possibility of applying adaptive generalized synchronization for identification, secure communication and sensing using complete adaptive synchronization.  
In future works, we will apply the developed approach to study other chaotic systems and also consider practical examples of applying adaptive generalized synchronization according to our findings. A more complete investigation of how symplectic methods can be used for the simulation of non-conservative chaotic systems will also be a topic of further investigation.  
Conceptualization, A.T. and D.B.; data curation, T.K. and O.D.; formal analysis, A.K.; funding acquisition, D.B.; investigation, A.K., A.T., T.K. and O.D.; methodology, A.K., A.T. and D.B.; project administration, D.B.; resources, T.K. and D.B.; software, A.K., A.T. and O.D.; supervision, D.B.; validation, T.K., O.D. and D.B.; visualization, A.K., A.T. and T.K.; writing--original draft, A.K., A.T. and T.K.; writing--review & editing, D.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Russian Foundation for Basic Research (RFBR), grant number 19-07-00496.  
This article does not contain any studies with human participants or animals.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.  
The authors declare no conflict of interest.