On the stability of positive nonlinear systems: Cooperative and concave system dynamics with applications to distributed networks

The most general class of systems we consider in this thesis is associated to sub-homogeneous vector fields, which includes as a special case concave vector fields. Conditions on the existence and uniqueness of an equilibrium point in the interior of the positive orthant are given and an estimate of the domain of attraction is made. We consider systems with irredubile, or reducible Jacobian matrix if the system is distributed