This article is cited in 3 papers

Local and global properties of nonautonomous dynamical systems and their application to competition models

V. G. Il'ichev

Rostov State University

Abstract: We develop the inheritance principle for local properties by the global Poincare mapping of nonautonomous dynamical systems. Namely, if a semigroup property is uniformly locally universal then it is enjoyed by the global Poincare mapping. In studying the global dynamics of competitors in a periodic medium, the crucial role is played by the multiplicative semigroup of the so-called sign-invariant matrices. We give geometric criteria for stability of equilibria (periodic solutions) in competition models.

Keywords: universality, semigroup, coarseness, sign-invariant matrices, competition, global stability.

UDC: 517.711.2:577.4

Received: 24.04.2001

 English version: Siberian Mathematical Journal, 2003, 44:3, 490–499

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