Balanced harvesting of dynamical discrete Ricker & Beverton-Holt system

In this paper, we discuss a dynamic version of the Ricker & Beverton-Holt (R & B-H)model, which states a two populations commercial fishery, where stock-recruitment effects cannot be neglected. We investigate a stable and balanced fish catches strategy that local breeding stocks are preserved abundant and stable. The Ricker & Beverton-Holt model in commercial fishery, based on the Allee effect, is combined by Beverton-Holt Logistic equation and Ricker model, ������������+1 = ������������������ ������ 1 + ������������������ -������������ ������������������ , ������������+1= ������-������������. 1 + ������������������ where the parameters ������, ������, ������, ������, are positive real numbers and the initial values ������0, ������0 are arbitrary nonnegative real numbers. Using the mean value theorem and Lyapunov functional skills, we obtain the sufficient conditions to guarantee the bounded and persistent solution of the Ricker & Beverton-Holt model, and global asymptotic stability of the equilibrium. Moreover, three numerical examples are given to elaborate on the results.