There is a way with Dynare to study complex dynamics in a DSGE model ?
For example, the presence of bifurcations, analysis of the stability of equilibria or complex dynamics.
I am aware that this would go against the concept of DSGE in general, but is there a way to study such dynamics in a model (probably making it with deterministic simulation) with Dynare?

Thank you for your answer.
I have tried a lot to understand however how to implement this in a dynare model.
Matlab usually allows you to carry out the analysis through two types of graphs: the Cobweb Graph, to study the equilibrium path and then the Bifurcation Diagram, by modifying the parameters and initial conditions.
So once you have written a DSGE model, following a Backward-Looking technique, what would be the “programming-way” to study these dynamics with Dynare? Is it possible to obtain these kind of graphs?
I searched a lot in the forum for any examples or reference models to understand how to program it but unfortunately I did not find anything.

Dear @jpfeifer
When I simulate according to this model, I obtain the trajectories (with rplot command equivalent to the link https://www.johndcook.com/blog/2020/01/19/cobweb-plots/. (then I understand that it is necessary to follow the Matlab programming to obtain the Cobweb graph (but doing another kind of script))

Trying to do that to a complete DSGE model I instead obtain for example these kind of trajectories with rplot command for some of my variables by imposing in stoch_simul the command periods=150 (minimum to obtain the rplot graph).

Being very difficult to understand the presence of chaotic dynamics in these kind of graphs obtained with longer periods,then the only way is so to program any function in another Matlab script to plot its graph (as explained by https://www.johndcook.com/blog/2020/01/19/cobweb-plots/) ?

So, I will try to follow your file above to replicate these kind of dynamics with a Backward-Looking perfect foresight technique applied to my models.
Really thank you very much for your help @jpfeifer