Abstract:
We suggest an “inheritance principle” according to which local properties are inherited by the global shift mapping. The principle is based on the notions of roughness and semigroup. When analyzing general competition models, key inherited properties (sign-invariant structures etc.) are determined. This approach is used to prove the global stability of periodic modes in a number of nonlinear nonautonomous ecological models.
Keywords:roughness, inheritance, stability, global shift mapping, Poincaré period map, dynamics of interaction of $n$ competitors, Hadamard's lemma, sign-invariant structure, dynamics of ecological communities.
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