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

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.