Quasi-periodic solutions of the Lotka-Volterra competition systems with quasi-periodic perturbations
The authors study an \(N\)-species Lotka-Volterra competition systems with quasi-periodic coefficients. Through constructing a Newton iteration they prove an abstract KAM theorem. Then they confirm the existence of positive quasi-periodic solutions for these LV systems. 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.
scientific article; zbMATH DE number 6052995