Error in Chaotic attracter

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lilly lord
lilly lord el 24 de Feb. de 2021
Comentada: Walter Roberson el 24 de Feb. de 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 comentarios
lilly lord
lilly lord el 24 de Feb. de 2021
% Initialize
t0=c-6/(1+x0^2+y0^2);
w(1)=1+u*(w0*cos(t0)-s0*sin(t0));
s(1)=u*(w0*sin(t0)-s0*cos(t0));
x(1)=1-a*s0^2+b*w0;
y(1)=mu*w0*(1-s0);
%%%%%%%fot one indexing
% Simulate
for i=1:n
t(i)=c-6/(1+x(i)^2+y(i)^2);
w(i+1)=1+u*(w(i)*cos(t(i))-s(i)*sin(t(i)));
s(i+1)=u*(w(i)*sin(t(i))-s(i)*cos(t(i)));
x(i+1)=1-a*s(i+1)^2+b*w(i+1);
y(i+1)=mu*w(i+1)*(1-s(i+1));
end
plot(x,y,'.','MarkerSize',4);
Modified but got even worst image
Walter Roberson
Walter Roberson el 24 de Feb. de 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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