Local and Global Properties of Nonautonomous Dynamical Systems and Their Application to Competition Models |
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Authors: | Il'ichev V G |
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Institution: | (1) Rostov State University, Rostov-on-Don |
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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. |
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Keywords: | universality semigroup coarseness sign-invariant matrices competition global stability |
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