8. Conclusions

Mixing problems are interesting sources for applied research in mathematical modeling, ODE, and linear algebra, and—as it was shown—their behavior depends on how they are connected. It has been proved that null eigenvalues are not expected in open systems with three or less components, and is a general conclusion for open MP-matrices that can be obtained by applying the Gershgorin circle theorem.

As a final remark, all the MP differential equation systems considered in this chapter have stable or asymptotically stable solutions. Nevertheless, this situation may change depending on the answers to the questions and the conjecture presented in the last section, giving a challenging proposal for further research on this topic.
