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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Il'ichev, V.G. Local and Global Properties of Nonautonomous Dynamical Systems and Their Application to Competition Models. Siberian Mathematical Journal 44, 490–499 (2003). https://doi.org/10.1023/A:1023816915603
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DOI: https://doi.org/10.1023/A:1023816915603