The LaSalle's invariant sets for a class of Lotka-Volterra prey-predator chain systems

Abstract Liu, Lu and Wang (1991) introduced a method for determining the LaSalle's invariant sets of Lotka-Volterra prey-predator chain systems. The current paper modifies their method and combines it with resultant and Grobner basis techniques. For a class of 8-dimensional Lotka-Volterra prey-predator chain systems, the necessary and sufficient conditions for their global stability are obtained.