I am trying to solve the following system of differential equations, which depend on three parameters, namely lambda, sigma0, sigma a. The final goal is to find a parameter triple, which fits the function sqrt[0.3166*(1+z)^3+0.6847] on the interval z=(0,3).
So far, I managed to plot the solution of the system of differential equations via Manipulate. But finding a parameter triple, for which the solution fits, seems quite tedious. Is there a way to do this systematically, or only trial and error? I attach what I have so far.
