Periodic Orbits in Periodic Discrete Dynamics
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 function...
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| Format: | article |
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2008
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| Online Access: | http://hdl.handle.net/11073/16688 |
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| Summary: | 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. |
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