三维Lotka-Volterra 系统正拟周期解的存在性和稳定性

The Existence and Stability of Positive Quasi-Periodic Solutions for the 3-Dimensional Lotka-Volterra System

中文关键词:  Lotka-Volterra系统  正拟周期解  KAM理论  牛顿迭代  李雅普诺夫泛函.

英文关键词:Lotka-Volterra system  positive quasi-periodic solution  KAM theory  Newton iteration  Lyaponov function.

中文摘要:

      这篇文章主要研究了三维Lotka-Volterra系统正拟周期解的存在性和稳定性.首先,我们利用KAM定理和牛顿迭代证明了在一个康拖集内三维Lotka-Volterra系统正拟周期解的存在性;再次我们利用李雅普诺夫泛函证明了上述解是稳定的.

英文摘要:

      This work focuses on the existence and stability of positive quasi-periodic solutions for the 3-dimensional Lotka-Volterra system. Using KAM (Kolmogorov-Arnold-Moser) theory and Newton iteration, it is shown that there exists a positive quasi-periodic solution in a Cantor family for the 3-dimensional Lotka-Volterra system. On the above basis, we can show the stability of the solution with the help of Lyapunov function.