Balanced harvesting of dynamical discrete Ricker & Beverton–Holt system

Abstract

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, yn+1=azn1+pzne−yn,zn+1=byn1+qyne−zn. where the parameters a,b,p,q, are positive real numbers and the initial values y0,z0 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.