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Periodic Orbits in Periodic Discrete Dynamics
Al-Sharawi, Ziyad
Al-Sharawi, Ziyad
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periodic_orbits.pdf
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Description
Abstract
We study the combinatorial structure of periodic orbits of nonautonomous difference equations π³βββ = πβ(π³β) in a periodically fluctuating environment. We define the ΣΆ-set to be the set of minimal periods that are not multiples of the phase period. We show that when the functions πβ are rational functions, the ΣΆ-set is a finite set. In particular, we investigate several mathematical models of single-species without age structure, and find that periodic oscillations are influenced by periodic environments to the extent that almost all periods are divisors or multiples of the phase period.