Abstract—This paper considers the existence and control of equilibrium (asymptotically stable) states in nonlinear positive normalized models (PNMs) functioning in the positive unit cube K in the space R n . The representation of a PNM as a functional graph is discussed. The author introduces the notion of admissible control as a control action whose coordinates belong to the interval [0,1], as well as establishes the convexity of the set of equilibrium states induced by admissible control actions. For PNMs with independent control and PNMs with linear state-feedback control, the model transition problem from an arbitrary initial state to a given equilibrium state is solved and the probability of such transition is defined. And finally, a numerical example illustrates all stages of the corresponding procedures.