We firstly introduce some recent results of Lotka-Volterra systems of three competing species, ODE system as well as PDE system. Then we mainly talk about the diffusive Lotka-Volterra systems, with theoretical arguments as well as some numerical calculation (simulation). A criteria for permanent coexistence in heterogeneous environments is obtained. It is proved that if the inter-competing strength is very weak, the system is always permanent, provided that each single one of the three species can survive in the absence of the two other species.
Biography
Benlong Xu is Professor at Mathematics and Science College of Shanghai Normal University. His research interests are partial differential equations and nonlinear analysis, especially nonlinear elliptic and parabolic PDEs, their applications and related theory in functional analysis.