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- Ziyad Alsharawi, James Angelos
- Applied Mathematics and Computation
- 2006

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… (More)

We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

- Ziyad Alsharawi
- Computers & Mathematics with Applications
- 2008

5 We study the combinatorial structure of periodic orbits of nonautonomous difference 6 equations xn+1 = fn(xn) 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 fn are rational functions, the Γ-set is a finite set. In 9 particular,… (More)

- Ziyad Alsharawi, Mohamed Ben Haj Rhouma
- Journal of biological dynamics
- 2009

In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton-Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic and conditional harvesting strategies. We find that for large initial populations, constant harvest is more beneficial to both the… (More)

We investigate the effect of constant and periodic harvesting on the Beverton-Holt model in a periodically fluctuating environment. We show that in a periodically fluctuating environment, periodic harvesting gives a better maximum sustainable yield compared to constant harvesting. However, if one can also fix the environment, then constant harvesting in a… (More)

- Ziyad Alsharawi, James Angelos, Saber Elaydi
- I. J. Bifurcation and Chaos
- 2008

In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xn = f(n− 1, xn−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)

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