Error in Chaotic attracter

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lilly lord 2021-2-24

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https://ww2.mathworks.cn/matlabcentral/answers/755224-error-in-chaotic-attracter

评论： Walter Roberson 2021-2-24

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 .

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lilly lord 2021-2-24

在 MATLAB Online 中打开

% 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 2021-2-24

在 MATLAB Online 中打开

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