How to plot coupling functions?

Want to plot these coupling functions r(t) and p(t) (in image) on a graph. I tried using this code and ended up with a blank graph(without errors) . Kindly help. Please note t varies as 2 to 3 with stepping of 0.01 .

z1 = -1.0629;
z2 = 0.5948;

%Code for r(t)
r_int1 = @(s) (2/3 - s).^(-1/2) .* (6 + abs(r(s))+abs(p(s))) ./ (5.*exp(s+4).*(1+abs(r(s))+abs(p(s))));
r_int2 = @(s) (t-s).^(-1/2) .* (6+abs(r(s))+abs(p(s))) ./ (5*exp(s+4).*(1+abs(r(s))+abs(p(s))));
r = @(t) ( z1.*t.^(-1/3)/gamma(1/2) .* integral(r_int1, 0, 2/3) ) + ( (1/gamma(1/2)) .* integral(r_int2, 0, t) );

%Code for p(t)
p_int1 = @(s) (3/2 - s).^(-4/5) .* (1/exp(2*s)) .* (sin(r(s))+sin(p(s))); 
p_int2 = @(s) (t - s).^(-4/5) .* (1/exp(2*s)) .* (sin(r(s))+sin(p(s)));
p = @(t) ( z2.*t.^(-3/2)/gamma(1/5) .* integral(p_int1, 0, 3/2) ) + ( (1/gamma(1/5)) .* integral(p_int2, 0, t) );

fp = fplot(r,p,[2 3]);
fp.Marker = '*';

[Cris LaPierre]

Without seeing your code, it's hard to say why your plot was empty.

[Toshith Vats]

Kindly check now I have upated

Answer 1

[Cris LaPierre]

If I don't use fplot, I do get a more descriptive error message. Based on the code you have shared, you are using your function handle r in you computation of r_int1 and r_int2 before it has been defined.

z1 = -1.0629;
z2 = 0.5948;

%Code for r(t)
r_int1 = @(s) (2/3 - s).^(-1/2) .* (6 + abs(r(s))+abs(p(s))) ./ (5.*exp(s+4).*(1+abs(r(s))+abs(p(s))));
r_int2 = @(s) (t-s).^(-1/2) .* (6+abs(r(s))+abs(p(s))) ./ (5*exp(s+4).*(1+abs(r(s))+abs(p(s))));
r = @(t) ( z1.*t.^(-1/3)/gamma(1/2) .* integral(r_int1, 0, 2/3) ) + ( (1/gamma(1/2)) .* integral(r_int2, 0, t) );

%Code for p(t)
p_int1 = @(s) (3/2 - s).^(-4/5) .* (1/exp(2*s)) .* (sin(r(s))+sin(p(s))); 
p_int2 = @(s) (t - s).^(-4/5) .* (1/exp(2*s)) .* (sin(r(s))+sin(p(s)));
p = @(t) ( z2.*t.^(-3/2)/gamma(1/5) .* integral(p_int1, 0, 3/2) ) + ( (1/gamma(1/5)) .* integral(p_int2, 0, t) );

% fp = fplot(r,p,[2 3]);
% fp.Marker = '*';
plot(r(2:.01:3),p(2:0.01:3))

Unrecognized function or variable 'r'.

Error in solution (line 5)
r_int1 = @(s) (2/3 - s).^(-1/2) .* (6 + abs(r(s))+abs(p(s))) ./ (5.*exp(s+4).*(1+abs(r(s))+abs(p(s))));

Error in integralCalc/iterateScalarValued (line 314)
fx = FUN(t);

Error in integralCalc/vadapt (line 132)
[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 87)
Q = integralCalc(fun,a,b,opstruct);

Error in solution (line 7)
r = @(t) ( z1.*t.^(-1/3)/gamma(1/2) .* integral(r_int1, 0, 2/3) ) + ( (1/gamma(1/2)) .* integral(r_int2, 0, t) );

[Toshith Vats]

Thanks for the help. Possibly, rearranging the order of equations would not help (leading to similar error ), could you please help me out in solving this issue.

[Toshith Vats]

Any hint regarding the solution for this problem would be helpful.

[Cris LaPierre]

The problem is you are using the function r inside your definition of r. It is possible to define recursive functions in MATLAB, but you need to have some sort of exit condition. Did you intend to define a recursive function, or are r(t) and r(s) in fact different functions?

[Toshith Vats]

They are recursive functions

[Cris LaPierre]

I'm not sure I've seen recursive integration before. Perhaps someone else can provide insight on that.

[Toshith Vats]

Thabnks fot the help