Error in Chaotic attracter

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lilly lord
lilly lord on 24 Feb 2021
Commented: Walter Roberson on 24 Feb 2021
Hi I am trying to plot the following equations
t_n = c - 6/(1+x_n ^2 + y_n^2);
w_n+1 =1+u*(w_n*cos(t_n)-s_n*sin(t_n));
s_n+1=u*(w_n *sin(t_n)-s_n*cos(t_n));
x_n+1=1-a*s_n+1^2 + b*w_n+1;
y_n+1 = mu*w_n+1*(1-s_n+1);
% where a=1.3; b=4; w= 0.1; s=0.1; c=0.4; u=0.9; mu=4;
the possible out come should be
Here is my code and the possible output
a=1.3; b=4; w= 0.1; s=0.1; c=0.4; u=0.9; mu=4;
x(1)=0.1;y(1)=0.1
n=10000;
% Initialize for n=0
%t(1)=0.4-(6/(1+x(1)^2+y(1)^2));
t(1)=0.4-(6/(1+s^2+w^2));
w(1)=1+u*(w*cos(t(1))-s*sin(t(1)));
s(1)=u*(w*sin(t(1))-s*cos(t(1)));
x(1)=1-a*s(1)^2 + b*w(1);
y(1) = mu*w(1)*(1-s(1));
for i=2:n
t(i)=c-(6/(1+s(i-1)^2+s(i-1)^2)); %% may replace with x and y
w(i)=1+u*(w(i-1)*cos(t(i))-s(i-1)*sin(t(i)));
s(i)=u*(w(i-1)*sin(t(i))-s(i-1)*cos(t(i)));
x(i)=1-a*s(i)^2+b*w(i);
y(i)=mu*w(i)*(1-s(i));
end
plot(x,y,'.','MarkerSize',4);
Here is the output.
Can anyone help me .
  4 Comments
Walter Roberson
Walter Roberson on 24 Feb 2021
Remember, the following is just changes to style, which also make the code more efficient.
Please check, though, the order that you initialize t w s x y. At the moment the order is important: you use the initial s value to compute t(1) and w(1) and then you assign to s(1) using the t values you calculated. If you changed the order you would get something different.
Perhaps you should be assigning to (2) indices at that point, and loop starting from 3 ?
a=1.3; b=4; c=0.4; u=0.9; mu=4;
n=10000;
x = zeros(1,n); y = zeros(1,n); t = zeros(1,n); w = zeros(1,n); s = zeros(1,n);
x(1) = 0.1; y(1) = 0.1; w(1) = 0.1; s(1) = 0.1;
% Initialize for n=0
t(1) = c-(6/(1+s(1)^2+w(1)^2));
w(1) = 1+u*(w(1)*cos(t(1))-s(1)*sin(t(1)));
s(1) = u*(w(1)*sin(t(1))-s(1)*cos(t(1)));
x(1) = 1-a*s(1)^2 + b*w(1);
y(1) = mu*w(1)*(1-s(1));
for i=2:n
t(i)=c-(6/(1+s(i-1)^2+s(i-1)^2)); %% may replace with x and y
w(i)=1+u*(w(i-1)*cos(t(i))-s(i-1)*sin(t(i)));
s(i)=u*(w(i-1)*sin(t(i))-s(i-1)*cos(t(i)));
x(i)=1-a*s(i)^2+b*w(i);
y(i)=mu*w(i)*(1-s(i));
end
plot(x,y,'.','MarkerSize',4);

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