how can i plot Bifurcation diagram and Lyapunov exponent for this code ?

Question

Samaa Yasser 2021-5-9

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/825690-how-can-i-plot-bifurcation-diagram-and-lyapunov-exponent-for-this-code

please i want a help to plot Bifurcation diagram and Lyapunov exponent for the proposed map (3D chaotic equation) , can anyone help me please to write me how can i plot them

%3D chaotic 
 x(1)=0.2350;
 y(1)=0.3500;
 z(1)=0.7350;
 a(1)=0.0125;
 b(1)=0.0157;
 l(1)=3.7700;
 image_height=256;
 for i=1:1:70000
     x(i+1)=l*x(i)*(1-x(i))+b*y(i)*y(i)*x(i)+a*z(i)*z(i)*z(i);
     y(i+1)=l*y(i)*(1-y(i))+b*z(i)*z(i)*y(i)+a*x(i)*x(i)*x(i);
     z(i+1)=l*z(i)*(1-z(i))+b*x(i)*x(i)*z(i)+a*y(i)*y(i)*y(i);
 end
 %%histogram equalization 
 x=ceil(mod((x*100000),image_height));
 y=ceil(mod((y*100000),image_height));
 z=ceil(mod((z*100000),image_height));
original=imread('peppers.jpg');
rgb=rgb2gray(original);
[row,col]=size(rgb);
n=500;
p=600;
q=700;
for j=1:1:row
    k(j)=x(j+n);
    l(j)=y(j+p);
end
for j=1:1:col*row
    m(j)=z(j+q);
end
for i=1:1:row
    for j=1:1:col
        if(mod(k(i),2)==0)
            if((j+k(i))<=col)   %shift right of row
               sh_row(i,j+k(i))=rgb(i,j);
               row_shift_even(i,j)=j+k(i);
            else
               sh_row(i,(j+k(i)-col))=rgb(i,j); 
               row_shift_even(i,j)=(j+k(i)-col);
            end
        else
            if((j-k(i))>=1)       %shift left of row
                sh_row(i,j-k(i))=rgb(i,j);
                row_shift_odd(i,j)=j-k(i);
            else
                sh_row(i,(col+j-k(i)))=rgb(i,j);
                row_shift_odd(i,j)=col+j-k(i);
            end
        end
    end
end
   
for j=1:1:col
    for i=1:1:row
        if(mod(l(j),2)==0)
           if((i-l(j))>=1)          %shift up of column
                sh_col(i-l(j),j)=sh_row(i,j);
                col_shift_even(i,j)=i-l(j);
            else
                sh_col((row+i-l(j)),j)=sh_row(i,j);
                col_shift_even(i,j)=row+i-l(j);
            end
        else
           if((i+l(j))<=row)           %shift down of column
               sh_col(i+l(j),j)=sh_row(i,j);
               col_shift_odd(i,j)=i+l(j);
               else
               sh_col((i+l(j)-row),j)=sh_row(i,j); 
               col_shift_odd(i,j)=(i+l(j)-row);
            end
        end
    end
end
total_length=row*col;
column_image=uint8(reshape(sh_col,1,total_length));
for i=1:1:total_length
xorr1(1,i)=bitxor(column_image(i),uint8(m(i)));
end
y=uint8(reshape(xorr1,row,col));