PERTURBATIONS IN LIVING STOCK AND SIMILAR BIOLOGICAL INVENTORY SYSTEMS

A differential-delay equation (1) is used to model controlled population dynamics of a closed biosystem consisting of n different co-habitating species. From the macroeconomical and ecological point of view the numbers of members of different biological species represent components of the vector of stock sizes in a very special kind of inventory system, and the corresponding problems will be treated similarly to the standard multipart inventory level optimization problems with quadratic cost functional. Through different control techniques the actual number of specimens of every species considered should be kept as close to the desired (equilibrium) levels as possible, at the simultaneous minimization of the control cost. The theoretical sensitivity results of the first author are generalized to the case of estimating the magnitude of changes in the total cost due to - possibly simultaneous - finite magnitude perturbations in system matrices and both types of delay, i.e. delays in the state and delays in the controls, since in many real-world systems such case is frequently encountered.