## 4 Discussion  
The authors conducted the study of two evolutionary approaches for constructing models of dynamical systems in the form of differential equations (EvolDE) and their  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Sample Size**} \\ \cline{2-10} \multirow{2}{*}{**No**} & \multicolumn{3}{c}{**150**} & \multicolumn{3}{c}{**100**} & \multicolumn{3}{c}{**50**} \\ \cline{2-10}  & & \multicolumn{6}{c}{**Noise, \%**} \\ \cline{2-10}  & **0** & **5** & **10** & **0** & **5** & **10** & **0** & **5** & **10** \\ \hline
1 & 0.034 & 0.036 & 0.039 & 0.032 & 0.037 & 0.039 & 0.03  
systems (EvolDES). According to the results, we can observe high accuracy of the models obtained as a result of testing. Changing the sample size within presented limits does not have a significant effect on the error.  
An important peculiarity of these approaches is the possibility of obtaining models in symbolic form. However, such representation is expected to be consistent with the true nature of the process. Therefore, it was determined that the models obtained as the identification of test tasks belong to three types: symbolically accurate (full compliance of the structure and parameters of the resulting equation or system with known true ones), symbolically conditionally accurate (the resulting structure corresponds to the known true one after performing the simplest mathematical operations), and approximate ones (solutions that do not belong to two previous types). Figures 7 and 8 show the number of symbolically accurate, symbolically conditionally accurate, and approximate solutions for each of the 50 runs for each task. Figure 7 contains information about the results for the evolutionary approach to the identification of dynamical systems in the form of an ODE. Figure 8 contains information about the results for the evolutionary approach to the identification of dynamical systems in the form of ODE systems.  
Figure 7: \(Cont.\)  
The successful search for a structure that corresponds to the true nature of the process is also proven by the above models of processes from chemistry and biology.  
The paper presents two evolutionary approaches that combine a genetic programming algorithm, differential evolution, and methods for the self-configuring parameters of evolutionary algorithms. The proposed approaches make it possible to identify dynamical systems in the form of ODEs and their systems. In the process of identification, both approaches automatically select the order, structure, and parameters of an ODE, both single and included in the system. The developed approaches make it possible to operate with systems in the form of ODEs of arbitrary order, a number of input and output variables.  
Figure 7: Symbolic accuracy of the resulting ODEs: (**a**) Data without noise; (**b**) Data with 5% of noise; (**c**) Data with 10% of noise.  
Figure 8: Symbolic accuracy of the resulting ODE systems: (**a**) Data without noise; (**b**) Data with 5% of noise; (**c**) Data with 10% of noise.  
**Author Contributions:** Conceptualization, E.S.; methodology, T.K. and E.S.; software, T.K.; validation, T.K. and E.S.; formal analysis, T.K. and E.S.; investigation, T.K. and E.S.; data curation, T.K.; writing--original draft preparation, T.K. and E.S.; writing--review and editing, T.K. and E.S.; visualization, T.K.; supervision, E.S.; project administration, T.K. and E.S.; funding acquisition, E.S. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the Ministry of Science and Higher Education of the Russian Federation within limits of state contract \(N\) FEFE-2020-0013.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.