In this paper, it is proved that the Hofbauer-So-Takeuchi conjecture for the global stability of a Lotka-Volterra system with discrete diffusion holds true in the case of 5. By using the computer algebra system Maple, and based on the modified PD algorithm proposed in the present paper, we check the positive definiteness of a class of polynomials in which the largest one has 4874376 terms.
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