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In this paper, we study the qualitative behavior of following open-access anchovy fishery model: xn+1=axnb-d α xvnyn, yn+1=yn(η(pαxvn-c)+1), where a,b,c,d,v,p,α, η, and the initial conditions x0, y0 are positive real numbers. More precisely, we investigate the necessary and sufficient condition for local asymptotic stability of the unique positive equilibrium point of this system. Some numerical examples are given to verify our theoretical results.