Yeah to describe this issue here, you just need a nonlinear ODE like u' = u^2 - u. Notice that if u > 1, then u' > 0 since u^2 > u. So then u will increase, which will make u' increase quadratically, rinse and repeat and you’ll go to infinity in essentially finite time (in terms of floating point at least). So bounding that initial condition is important for these autocatalytic models.
You shouldn’t need a cluster for this. Play with ideas like Solving Large Stiff Equations · DifferentialEquations.jl and devectorizing a bit.