The size dynamics of controlled populations

A system, invariant in a positive cone of a Euclidean space, of nonlinear differential equations is discussed which includes a wide range of models representing the size dynamics of controlled populations. Conditions for existence of a stable stationary solution are given. Bifurcation in the birth of a periodic solution is studied. The initial nonlinear system is associated with three linear control systems. The transfer functions of these linear systems determine stability or otherwise of periodic solution to the initial system.