On the periodic logistic equation
We show that the -periodic logistic equation ₙ₊₁ = μₙ mod ₙ(1 - ₙ) has cycles (periodic solutions) of minimal periods 1; ; 2; 3; …. Then we extend Singer’s theorem to periodic difference equations, and use it to show the -periodic logistic equation has at most stable cycles. Also, we present computa...
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| Format: | article |
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2006
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| Online Access: | http://hdl.handle.net/11073/16689 |
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| Summary: | We show that the -periodic logistic equation ₙ₊₁ = μₙ mod ₙ(1 - ₙ) has cycles (periodic solutions) of minimal periods 1; ; 2; 3; …. Then we extend Singer’s theorem to periodic difference equations, and use it to show the -periodic logistic equation has at most stable cycles. Also, we present computational methods investigating the stable cycles in case = 2 and 3. |
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