Ziyad Alsharawi

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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)
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 p divides k. When p is not a divisor of k, the periodic orbits depend on the periodic orbits of(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)
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