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We show that the p-periodic logistic equation x n+1 = µ n mod p x n (1 − x n) 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… (More)

5 We study the combinatorial structure of periodic orbits of nonautonomous difference 6 equations x n+1 = f n (x n) in a periodically fluctuating environment. We define the 7 Γ-set to be the set of minimal periods that are not multiples of the phase period. We 8 show that when the functions f n are rational functions, the Γ-set is a finite set. In 9… (More)

Existence and stability of periodic orbits of periodic difference equations with delays. Abstract In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays x n = f (n − 1, x n−k). We show that the periodic orbits of this equation depend on the periodic orbits of p autonomous equations when… (More)

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