On Topological Entropy of Interconnected Nonlinear Systems

We study topological entropy of a nonlinear system represented as an interconnection of smaller subsystems. Under suitable assumptions on the Jacobian matrices characterizing the interconnection, we obtain an explicit upper bound on the entropy of the overall system, and show that it can be related to upper bounds on the entropies of the subsystems. We also analyze in detail the special case of a cascade connection of two subsystems, establishing an upper bound on the entropy which is more tightly linked to individual entropy bounds for the subsystems.