Instability of Solutions of Volterra Type Systems Depending on the Asymptotic Localization of the Malthusian Vector

Abstract

We study the behavior of solutions of Volterra type systems for various versions of asymptotic localization of the Malthusian vector. In particular, it is proved that if the origin belongs to the boundary of a. convex set that is almost attracting for such a. vector calculated on a. solution and if the solutions are logarithmically bounded, then the minimum face of this set containing the origin is almost attracting for this vector as well. Applications of the results to problems arising in mathematical biology are considered.