For permanent and partially permanent, uniformly bounded Lotka–Volterra systems, we apply the Split Lyapunov function technique developed for competitive Lotka–Volterra systems to find new conditions that an interior or boundary fixed point of a Lotka–Volterra system with general species–species interactions is globally asymptotically stable. Unlike previous applications of the Split Lyapunov technique to competitive Lotka–Volterra systems, our method does not require the existence of a carrying simplex.
Lotka–Volterra systems Global attractors Global repellors Global asymptotic stability
Mathematics Subject Classification (2000)
34D05 34D20 34C11 92D25
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Liang X., Jiang J.: The dynamical behaviour of type-K competitive Kolmogorov systems and its application to three-dimensional type-K competitive Lotka–Volterra systems. Nonlinearity 16, 785801 (2003)MathSciNetCrossRefGoogle Scholar