| The Existence and Stability of Positive Quasi-Periodic Solutions for the 3-Dimensional Lotka-Volterra System |
| Received:July 03, 2012 Revised:October 12, 2012 |
| Key Words:
Lotka-Volterra system positive quasi-periodic solution KAM theory Newton iteration Lyaponov function.
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| Fund Project:Supported by the Ability Enhancement Projects of the National Basic Science Talent Trainning Fund (Grant No.J1103110). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.06.005 |
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