### Algorithm for Probability Distribution Variation Based on Graphical Language  
To tackle the challenge of flexibly setting probability distribution types for chaotic signals, this section introduces a graph-based algorithm for probability distribution transformation. Utilizing this algorithm, chaotic intrinsic signals can seamlessly undergo conversion into chaotic signals exhibiting the desired probability distribution type. Thus, the objective of the flexible adjustment of probability distributions for chaotic signals is effectively attained.  
Let the probability density function of the intrinsic chaotic signal \(x\) defined on \((a,b)\) be \(f_{x}(x)\), and its distribution function be \(F_{x}(x)\); let \(y\) be the chaotic signal with the expected probability distribution defined on \([c,d]\), with the probability density function \(f_{y}(y)\) and distribution function \(F_{y}(y)\).  
The graphical transformation from the intrinsic chaotic signal \(x\) to the target distribution chaotic signal \(y\) is illustrated in Figure 5.  
Figure 4: Waveform, probability density function, and distribution function of intrinsic signal \(x\): (**a**) waveform; (**b**) probability density function and distribution function.  
Figure 5: Probability distribution transformation algorithm of chaotic signals based on graphic language.  
According to Figure 5, the specific steps of the graphical-based chaotic signal probability distribution transformation algorithm are described as follows:  
Step 1: Choose an intrinsic chaotic signal \(x\) as the signal source, and let its domain be (a, b). Extract a sample of \(N\) independent identically distributed values, denoted as \(x_{1}\), \(\ldots\), \(x_{N}\).  
Step 2: Use the kernel density estimation algorithm as shown in Equation (1) to calculate its probability density function \(f_{x}(x)\), and then calculate the distribution function \(F_{x}(x)\).  
Step 3: Based on the probability distribution type of the expected probability distribution chaotic signal \(y\) (defined on the interval \([c,d]\)), calculate its probability density function \(f_{y}(y)\) and distribution function \(F_{y}(y)\).  
Step 4: Select M nodes in the interval \((a,b)\): \(x_{1}=a\), \(\ldots\), \(x_{i}\), \(\ldots\), \(x_{M}=b\). Using the graphical method shown in Figure 5 and following the principle of equal distribution function values, calculate the corresponding \(M\) nodes on the interval \([c,d]\) as \(y_{1}=c\), \(\ldots\), \(y_{i}\), \(\ldots\), \(y_{M}=d\).  
Step 5: By using piecewise linear interpolation, the analytical expression of the transformation relationship \(y=g(x)\) can be obtained  
\[g(x)=\sum_{j=1}^{M}y_{i}l_{j}(x) \tag{5}\]  
where the basis function \(l_{j}(x)\) is  
\[l_{j}(x)=\begin{cases}\frac{x-x_{j-1}}{x_{j}-x_{j-1}}&,\hskip 28.452756 ptx_{j-1} \leq x\leq x_{j}(j\
eq 1)\\ \frac{x-x_{j-1}}{x_{j+1}-x_{j}}&,\hskip 28.452756 ptx_{j}\leq x\leq x_{j+1}(j \
eq M)\\ 0&,\hskip 28.452756 ptx\in(a,b),\hskip 28.452756 ptut\hskip 28.452756 ptx\
otin[x_{j-1},x_{j+1}] \end{cases} \tag{6}\]  
Step 6: By using the transformation relationship \(y=g(x)\), the intrinsic signal \(x\) can be transformed into chaotic signals \(y\) with the desired probability distribution.  
In Appendix B, a set of parameter values for the analytical expression of the transformation relationship of transforming the chaotic signal of Chua into a uniform distribution chaotic signal composed of 100 nodes is provided (as shown in Tables A1-A3).  
In summary, the flexible setting strategy for the probability distribution of chaotic signals based on graphical language can be summarized as follows: firstly, using the principle that the distribution function values of \(x\) and \(y\) are equal to obtain corresponding pairs of points \((x_{i},y_{i})\); then, using the piecewise linear interpolation method to obtain the transformation relationship \(y=g(x)\); and finally, using the transformation relationship to transform the intrinsic signal \(x\) into the target chaotic signal \(y\).