The positive definiteness of a class of polynomials from the global stability analysis of Lotka-Volterra systems

In this paper, a class of Lotka-Volterra discrete diffusion systems is considered. A mechanical procedure for checking the positive definiteness of polynomials from the stability analysis of these diffusion systems is described. Some known results of lower-dimensional systems are checked and the Hofbauer-So-Takeuchi conjecture is proved in the case of n = 4 based on the proposed procedure and the computer algebraic system MATHEMATICA.