Optimal control and the simple logistic prototype: Three cases

A discrete dynamics optimum control problem is stated, which utilizes the simple logistic equation as its deterministic underlying equation of motion. Three specific cases are studied, simple enough to afford analytical treatment. It is shown that when aversion to oscillations in both the state variable and the controlling parameter are assumed, then over a time horizon involving three time periods, the optimum solution may involve thresholds in the relative weight of these two types of oscillations. Up to that threshold, the control problem may be simple; whereas, beyond that threshold, management may become complicated.