## 3 Results  
Let us consider the proposed approaches in detail. Firstly, consider the efficiency on test tasks represented by ODEs and their systems. The tasks presented in Table 1 were used to test the evolutionary approach of EvolDE. ODEs represent tasks of various types and orders. The exhaustive testing and study of the efficiency of this algorithm on tasks with some input variables and with input variables represented by functions are reflected in [25]. Table 2 presents the results of identification according to the data generated by the tasks from Table 1. Data of different volumes were generated without noise and with noise for each task. Noise is distributed normally. The authors conducted 50 runs for each task. Table 2 shows the results by error values (averaged over 50 runs) depending on the sample size and the presence of noise in the data. \begin{table}
\begin{tabular}{c c} \hline \hline
**No** & **Differential Equation** & **Initial Sample Point** \\ \hline
1 & \(y^{\prime}=\frac{y+x^{2}\cos x}{x}\) & \(y(x_{0})=0.06\) \\ \hline
2 & \(y^{\prime}=-\frac{y\ln y}{x}\) & \(y(x_{0})=c\) \\ \hline
3 & \(y^{\prime}=\frac{2(y^{\prime})^{2}}{y-1}\) & \(y(x_{0})=2\) \\ \hline
4 & \(y^{\prime}=6y^{\prime}-9y+6 xe^{3x}\) & \(y(x_{0})=3\) \\ \hline
5 & \(y^{\prime\prime}=4y^{\prime}+24c^{2x}-4\cos(2x)+8\sin(2x)\) & \(y(x_{0})=1\) \\ \hline
6 & \(y^{IV}=y+2\cos(x)\) & \(y(x_{0})=0\) \\ \hline
7 & \(y^{V}=y^{IV}+2x+3\) & \(y(x_{0})=2\) \\ \hline
8 & \(y^{\prime}=\frac{y+x_{1}^{2}\cos x_{2}}{x_{3}}\) & \(y(\overline{x}_{0})=0.06\) \\ \hline
9 & \(y^{\prime}=\frac{y^{\prime}+x_{2}^{2}yy^{\prime}}{x_{2}^{2}}\) & \(y(\overline{x}_{0})=0\) \\ \hline
10 & \(y^{\prime}=-2y^{\prime}-2y+2x_{1}^{2}+8x_{2}+6\) & \(y(\overline{x}_{0})=3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test tasks for the evolutionary approach to the identification of dynamical systems in the form of an ODE. The authors consider the dependence of the rate of a chemical reaction on temperature to study the possibility of using this approach in solving applied tasks. A set of values describing the process for a chemical reaction is known. It is necessary to construct a model that describes a change in the rate of a chemical reaction depending on temperature. It is necessary to estimate the dependence of the reaction rate constant on temperature for the reaction \(H_{2}+I_{2}\to 2 HI\). A sample of temperature (T) and rate constant (\(k\)) values was applied to construct a model. The sample size was 12 points. As a result, the authors obtained a symbolic model. It corresponds to the well-known Arrhenius Equation (7):  
\[\frac{dlnk}{dT}=\frac{E_{a}}{RT}, \tag{7}\]  
where \(E_{a}\) is the activation energy, and \(R\) is the universal gas constant [26]. Figure 5 shows graphs corresponding to the original data and points obtained from the model. The mean squared error of the fit was 0. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Sample Size**} \\ \cline{2-9}  & & **150** & & **100** & & **50** & \\ \cline{2-9}
**No** & & & & & & & & \\ \cline{2-9}  & **0** & **5** & **10** & **0** & **5** & **10** & **0** & **5** & **10** \\ \hline
1 & 0 & 0 & 0.001 & 0 & 0 & 0 & 0 & 0.0001 \\
2 & 0 & 0 & 0 & 0 & 0 & 0 & 0.0001 & 0.0001 \\
3 & 0.0001 & 0.0008 & 0.0008 & 0.0001 & 0.0008 & 0.0008 & 0.0002 & 0.0009 & 0.0012 \\
4 & 0.0002 & 0.0003 & 0.0003 & 0.0002 & 0.0003 & 0.0003 & 0.0004 & 0.0005 \\
5 & 0 & 0.0005 & 0.0007 & 0 & 0.0006 & 0.0007 & 0.0001 & 0.0008 & 0.0008 \\
6 & 0 & 0.0001 & 0.0002 & 0 & 0.0002 & 0.0003 & 0.0001 & 0.0004 & 0.0005 \\
7 & 0 & 0.0008 & 0.0009 & 0.0001 & 0.0009 & 0.0009 & 0.0001 & 0.0013 & 0.0014 \\
8 & 0.0046 & 0.0055 & 0.0059 & 0.0074 & 0.0092 & 0.0104 & 0.0113 & 0.0201 & 0.0287 \\
9 & 0.0017 & 0.0047 & 0.0053 & 0.002 & 0.0049 & 0.0051 & 0.0033 & 0.0058 & 0.0075 \\
10 & 0.0011 & 0.0033 & 0.0041 & 0.0023 & 0.0037 & 0.0042 & 0.0024 & 0.0037 & 0.0039 \\ \hline \hline \end{tabular}
\end{table}