Optimal harvesting policy for the Beverton--Holt model

Abstract

In this paper, we establish the exploitation of a single population modeled by the Beverton--Holt difference equation with periodic coefficients. We begin our investigation with the harvesting of a single autonomous population with logistic growth and show that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, we approach the investigation of the optimal harvesting policy that maximizes the annual sustainable yield in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model. In the second part of the paper, we formulate the harvested Beverton--Holt model and derive the unique periodic solution, which globally attracts all its solutions. We continue our investigation by optimizing the sustainable yield with respect to the harvest effort. The results differ from the optimal harvesting policy for the continuous logistic model, which suggests a separate strategy for populations modeled by the Beverton--Holt difference equation.

Risk sensitivity in Beverton–Holt fishery with multiplicative harvest

“…The optimal survival rate that yields maximum sustainable catch is consistent with the result of an equivalent model discussed in [11] (see Theorem 3.9), derived for an equivalent form X t +1 (1 + h t ) = G (X t ). The corresponding (equilibrium) maximum sustainable yield C * e and maximum yield sustainable population X * e are, using ( 6) and ( 9), given by…”

“…We note that, thanks to the recent results of Bohner and Streipert [11], the methodology and findings presented in this section can be extended to the more general ω−periodic case, for ω > 1. Conceptually, the problem remains the same but associated algebraic expressions could become more complex, which could be considered in future work.…”

“…This is discussed in the next section. We note that the authors of [11] did not consider any stochastic setting.…”

Optimal harvesting policy for the Beverton-Holt quantum difference model

“…This allows us to investigate the harvest effort reduced by the time stretching property. Applying the substitution α = v−1 µv to (9), we obtain (10) x(qt) =…”

“…Then (2) has a unique ω-periodic solution which globally attracts all its solutions. Theorem 1.2 (See [10]). Assume (3) and (in order to guarantee a nonnegative harvest effort)…”