Stabilizability and controllability of the reproduction process (Q802518)

Conditions are described for the existence of stationary modes of nonlinear control processes that define the reproduction dynamics of populations and communities under limiting conditions. In the specific situation the phase coordinates of the differential equations as well as the control actions assume only nonnegative values. Global stabilizability is shown to be possible for stationary solutions with the aid of feedback having a variable structure and containing a zero on the boundary of permissible control values. Global controllability of these processes is shown to be possible with the aid of open-loop nonnegative control when the conditions of position generality in the vicinity of stationary points are satisfied.