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The Positive Definiteness of a Class of Polynomials from the Global Stability Analysis of Lotka-Volterra Systems

Z. Lu
G. Wang
Journal / Anthology

Computers and Mathematics with Applications
Year: 1999
Volume: 38
Page range: 19-27

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.

*Mathematics > Calculus and Analysis > Differential Equations