This paper analyzes the existence conditions of a nonnegative global stable equilibrium point in generalized Lotka-Volterra systems with diffusion for a patchtype environment. Applying the extended stability theory of LaSalle and complementarity theorem, several structures of patches with a globally stable equilibrium are derived. It is shown that diffusion cannot be destabilizing for systems with such structures. © 1986.
Takeuchi, Y. (1986). Global stability in generalized Lotka-Volterra diffusion systems. Journal of Mathematical Analysis and Applications, 116(1), 209–221. https://doi.org/10.1016/0022-247X(86)90053-3