Magno Enrique Mendoza Meza

Exploitation of a single species by a threshold management policy.

Continuous time models of single exploited populations usually generate outcomes expressing a dependence of yield and economic items on harvest intensity. In this work it is shown that a known threshold policy is able to generate yield and related economic items that do not depend on harvest intensity, but rather on the values of the population threshold itself and the species intrinsic parameters. It is argued that since this result can be carried over to other models of single species dynamics, it may have significant implications in the management and conservation of exploited populations.

Controlling predator–prey discrete dynamics utilizing a threshold policy with hysteresis

Abstract This paper introduces a threshold policy with hysteresis (TPH) for the control of the logistic one-species model, the Lotka–Volterra and Rosenzweig–MacArthur two species density-dependent predator–prey models. A nonstandard scheme is used for the discretization of the models since it results in preservation of the qualitative characteristics of the continuous-time models. Two theorems that establish the global stability of the discrete logistic model subject to the threshold policy (TP) and the TPH are proved. The proposed policy (TPH) is more realistic than a pure threshold policy (TP) proposed earlier in the literature and changes the dynamics of the system in such a way that a low amplitude bounded oscillation, far from the extinction region, is achieved. Furthermore, it can be designed by a suitable choice of so called virtual equilibrium points in a simple and intuitive manner.