Abstract
We show that the 𝒑-periodic logistic equation 𝒳ₙ₊₁ = μₙ mod 𝒑𝒳ₙ(1 - 𝒳ₙ) has cycles (periodic solutions) of minimal periods 1; 𝒑; 2𝒑; 3𝒑; …. Then we extend Singer’s theorem to periodic difference equations, and use it to show the 𝒑-periodic logistic equation has at most 𝒑 stable cycles. Also, we present computational methods investigating the stable cycles in case 𝒑 = 2 and 3.
