The basic model type determines the factors that can become effective in a growth model, for example in a simple neoclassical model, a two-sector model of endogenous growth or a standard AK model, etc. Determining factors can be differences in sectoral capital stocks, population growth, the development of consumption and savings rates, wage development, production technology and the accumulation of human capital (education, knowledge, research and development). All of these factors determine the transition dynamics and, in multi-country comparisons, the speed of convergence. Countless literature references can be found in any search engine under the heading of transition dynamics.

There is also labor productivity, health as a component of human capital as well.

The key problem is that too little research effort is given to traverse analysis, i.e. the disequilbrium process to move from onevequilibros state to another. Butbthis is essential to understand development. Change is not a movement towards a persistent stable equilibrium. It is is just the opposite.

If the model has linear with all unit values less than one plus if there exists pairs of complex unit values which leads to fluctuations.

If the model is truely non-linear the transitional dynamics are much leas easily predictable. Just think of the limit-cycle models of Goodwin.

Article The Goodwin model revisited: Hopf bifurcation, limit-cycle, ...

Furthermore the transitional dynamics depends on the starting values of the model.

Most stable linear models face the problem that they have steady state path but the starting values differ from the implicit steady state. This is essential for is transition process. The simulation just follow the model dynamics by adjusting to the steady state of the model.

The Nonlinear Accelerator and the Persistence of Business Cycles

https://www.jstor.org/stable/1907905

In the Richard Goddwin model there is not a steady state but instead limit cycles.

Article Transitional Dynamics and Economic Growth in the Neoclassical Model

Transitional Dynamics and Economic Growth in the Neoclassical Model

For the properties of the neoclassical growht model see e.g. the article above.