Simulating a ball travelling down an incline

So the difference between those two cases is the coefficient of friction $mu$. If $mu=0$ then it is pure slipping, so the dynamics is described as if a point mass was on the incline.

However, if $mu>0$ then you have to track the angular velocity of the disc $omega(t) = frac{mu N}{I}t$ where $N$ is the normal force. If that velocity reaches the condition $omega = frac{v}{R}$ then there is no more slipping and you have to change the equations of motion in the simulation.

Each case, however, gives a different formala for the force imparted by the contact of the ball with the incline.

Unfortunately, that isn’t really avoidable. In the case of slipping, the friction force is given by the kinetic friction formula which is a standard equality. In contrast, in the case of rolling, the friction force is given by the the static friction formula which is an inequality. That cannot be solved so easily. It requires the use of constraints in order to get a unique value.

try to determine if the ball is rolling or not and apply the appropriate formula

That's what I would do.

As stated in your linked page, slipping occurs when $v_mathrm{cm}-omega Rneq 0$.

You'll also have to keep track of (i) switching between kinetic and static friction and (ii) also work out what your max static friction is.

Consider the force pushing the ball (mass $m$, radius $r$) down the ramp (angle $theta$, friction coefficient $mu$): $F_g=mg sin (theta)$; and the force pushing the opposite direction: $F_f$, which is negative in our convention. For the linear acceleration, we have $F_g + F_f=ma$, and for the angular acceleration we have $F_fr=Ialpha$. Let's say the ball is solid so that the moment of inertia is $I=frac{2}{5}mr^2$ (we could as easily do a hollow ball--then we'd use $I=frac{2}{3}mr^2$).

Assume for the moment that the ball rolls without slipping. Then $alpha=-frac{a}{r}$. This with the stuff above gives $F_{f_{rolling}}=-frac{2}{7}mgsin(theta)$.

Now, the maximum magnitude achievable for friction occurs when $F_f=F_{f_{max}}=-mu N=-mu mg cos(theta)$. The actual frictional force that acts will be whichever of $F_{f_{rolling}}$ and $F_{f_{max}}$ is smaller in magnitude. (Note: $N=mgcos(theta)$ is the normal force.)

So, you just need to check whether the slope the ramp--that is, $tan(theta)$--is greater or less than $frac{7}{2}mu$. If less, use $F_f=-frac{2}{7}mgsin(theta)$; if more, use $F_f=-mu mg cos(theta)$.