The global stability of a Lotka-Volterra system with discrete diffusions

Article type: Research Article

Authors: Yang, Ming^{a; b} | Yang, Jing^{a; b} | Lu, Guichen^c | Lu, Zhengyi^{d; *}

Affiliations: [a] Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu, Sichuan 610041, China | [b] University of Chinese Academy of Sciences, Beijing 100049, China | [c] School of Science, Chongqing University of Technology, Chongqing 400054, China | [d] School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan 610068, China

Correspondence: [*] Corresponding author: Zhengyi Lu, School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan 610068, China. E-mail: [email protected].

Abstract: 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 n= 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.

Keywords: Lotka-Volterra systems, discrete diffusion, modified PD-algorithm, Hofbauer-So-Takeuchi conjecture

DOI: 10.3233/JCM-193694

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 20, no. 1, pp. 121-132, 2020