Controlability of quasimonotone systems in a positive cone

The controllability problem is solved for quasimonotone systems with control signals which vanish on the range boundary. Quasimonotoneity implies that the nondiagonal elements in the Jacobian matrix of the right-hand side are nonnegative. The set of initial states is constrained by vectors of a Euclidean state of nonnegative components. The problem statement is motivated by biological applications.