Global Dynamic Behavior for Lotka-Volterra Systems with a Reducible Interaction Matrix

Recently, Redheffer obtained a global stability result of a positive equilibrium point for a class of Lotka-Volterra systems with reducible interaction matrices. The present paper, following his proving method, extends his result in some sense and gives examples showing complicated global asymptotic behaviours of solutions of the systems, in which the LaSalle invariant set can have nonconstant periodic solutions