Аннотации:
We consider the problem on the stability of the Oskolkov equations, defined on a finite connected directed graph with the continuity and flow balance conditions at the vertices, with parameters λ0, ν, e{open} ∈ ℝ+. We show that if λ ≤ λ0, then the solutions with initial data in some neighborhood of zero are uniformly asymptotically stable. But if λ > λ0, then there arises a one-dimensional unstable invariant manifold. © 2010 Pleiades Publishing, Ltd.