In this thesis we study genetic regulatory networks using a minimal nonlinear
model from literature and extend this to multi-compartment gene-to-gene interaction networks using both numerical simulations and random matrix theory.
When we add perturbations to a system of two interaction networks, the largest
eigenvalue becomes larger, which means the system is more likely to be unstable.
It turns out that for a certain region of values of random matrix variables,
we can predict the change of their eigenvalues caused by a perturbation with
perturbation theory. We quantify the stability of the genetic regulatory network
models, where the dynamics is largely governed by random matrices, with maximal Lyapunov exponents (MLE's). We have been able to compute these MLE's
when the model is considered with certain constraints. At last, we research the
correlation between the connectivity of two networks describing such models
and their KL divergence. Here we conclude that the KL divergence between
two networks goes up when the connectivity of one of the networks gets larger.
We conclude that for possible follow-up research more advanced programs are
needed with longer running simulations.