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03/07/2008, 15:00 — 16:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University*

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Attenuance vs. Resonance of populations in fluctuating environment

A lingering question in biology has been whether periodic fluctuation of the environment would lead to attenuance or resonance. Such a question is of paramount importance in pest control and many environmental issues. To address this question and related issues, the speaker and Robert Sacker developed a mathematical theory, the theory of periodic dynamical systems. Its main tool is the construction of an associated discrete skew-product dynamical systems. An extension of the theory to unimodal maps with Allee effect is now under development.