Fitting differential equation (ode45) to data using lsqcurvefit

I'm trying to fit an ode to data. For now I only have data I generated, so I know if I'm fitting it correctly. I found another thread about fitting ode to data using lsqcurvefit and followed that but couldn't get my code to give me the correct parameters.

Here is my code:

a = 1.5; 
sa = .8; 
n = .3; 

% generates the data I will fit to
func = @(t,x) = ((1-x)*sa*(x^a)) - (x*(1-sa)*((1-x)^a)); 
tspan = 1:40; 
[t1, x1] = @ode45(func, tspan, n); 

% trying to find a and sa values that will fit the data generated 
x0 = [.3 .3]; 
v = lsqcurvefit(@ASModelODE, x0, t1, x1); 

function s = ASModelODE(v,t)
  % ode:
  %      dx/dt = (1-x)*sa*x^a - x*(1-sa)*(1-x)^a 
  % variables:
  %      x
  % parameters: 
  %      v(1) = sa, v(2) = a; 

      x0 = [0.1 0.1]; 
      diffeq = @(t,x) (1-x).*v(1).*x.^v(2) - x.*(1-v(1)).*(1-x).^v(2); 
      [T, Sv] = ode45(diffeq, t, x0)
      s = Sv(:,1); 
 end

when I run this I get errors like "Complex sparse QR is not yet available" and it also gives me imaginary fit parameters most of the times.

What am I doing wrong?

Answer 1

[Torsten]

Most probably, the solution of your differential equation T becomes greater than 1. This will turn (1-T)^v(2) into a complex number.

Best wishes

Torsten.