From stagnant equilibrium to growth equilibrium

Recently, I try to replicate Issac and Kim (2005) .
In the paper, there are two different equilibrium. One is stagnant, and the other one is growth equilibrium.

In stagnant equilibrium, the investment in human capital is zero: h=0.
In growth equilibrium, the investment in human capital is a function.
If we have a large enough exogenous shock in some period, then we can get rid off stagnant equilibrium.
The investment in human capital is from zero to a function.
The function of accumulation of human capital will change.

Is it possible for dynare to simulate the dynamic transition from stagnant to steady growth due to exogenous shock under different functions of human capital?
Thanks for your kindly help in advance.