Periodic Orbits in Periodic Discrete Dynamics - Al-Sharawi, Ziyad (2008)
We study the combinatorial structure of periodic orbits of nonautonomous difference equations ₙ₊₁ = ₙ(ₙ) in a periodically fluctuating environment. We define the Ӷ-set to be the set of minimal periods that are not multiples of the phase period. We show that when the functions ₙ are rational functions, the Ӷ-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.