# American Institute of Mathematical Sciences

July  2012, 17(5): 1537-1550. doi: 10.3934/dcdsb.2012.17.1537

## Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations

 1 School of Mathematical Sciences, Soochow University, Suzhou 215006, China, China, China

Received  November 2010 Revised  January 2012 Published  March 2012

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.
Citation: Qihuai Liu, Dingbian Qian, Zhiguo Wang. Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1537-1550. doi: 10.3934/dcdsb.2012.17.1537
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