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.  
Fund Project:Supported by the Ability Enhancement Projects of the National Basic Science Talent Trainning Fund (Grant No.J1103110).
Author NameAffiliation
Gang HUANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Wenbo LI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Shouxia LU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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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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