Abstract
The paper investigates the stability of the Lotka — Volterra dynamic system ≪predator — two preys≫ with the help of variational method. This method is applicable for studying equilibrium stability non-linear dynamical systems of any kind and in any dimension. It approves its effectiveness even in cases where the use of the Lyapunov function causes great difficulties (for example, when solving tasks of large dimension). The proposed method is based on a variation method for estimating the rate of phase-state metric change for the perturbed system when the variable t → ∞. The disadvantage of the variation method is the fact that this method provides only the necessary conditions of stability. However, its it forms the first step in studying the stability of non-linear dynamical systems of any kind and any dimension.
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