Stabilizability and controllability of the reproduction process

The paper describes conditions for existence of stationary modes for nonlinear control processes which specify the dynamics of population and community reproduction with the resources being limited. The situation is specific in that the phase coordinates of differential equations take on only nonnegative values. Stationary solutions are shown to be stabilizable by a feedback whose structure is variable and contains a zero on the boundary of admissible values of the control functions. The processes are shown to be globally controllable when openloop control is used and the conditions of position generality in the vicinity of stationary points are satisfied.