QUASI-PERIODIC SOLUTIONS OF THE LOTKA-VOLTERRA COMPETITION SYSTEMS WITH QUASI-PERIODIC PERTURBATIONS

摘要

In this paper, we prove the existence of positive quasi-periodic solutions for the Lotka-Volterra competition systems with quasi-periodic coefficients by KAM technique. The result shows that, in most case, quasi-periodic solutions exist for sufficiently small quasi-periodic perturbations of the autonomous Lotka-Volterra systems. Moreover, these quasi-periodic solutions will tend to an equilibrium of the autonomous Lotka-Volterra systems.