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The dynamics of some discrete models with delay under the effect of constant yield harvesting

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  • Abu-Saris, Raghib
  • AlSharawi, Ziyad
  • Rhouma, Mohamed Ben Haj

Abstract

In this paper, we study the dynamics of population models of the form xn+1=xnf(xn−1) under the effect of constant yield harvesting. Results concerning stability, boundedness, persistence and oscillations of solutions are given. Also, some regions of persistence and extinction are characterized. Pielous equation was considered as an example on these models, and a connection with a Lyness type equation has been established at certain harvesting level, which is used to give an explicit description of a persistent set.

Suggested Citation

  • Abu-Saris, Raghib & AlSharawi, Ziyad & Rhouma, Mohamed Ben Haj, 2013. "The dynamics of some discrete models with delay under the effect of constant yield harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 26-38.
    • Handle: RePEc:eee:chsofr:v:54:y:2013:i:c:p:26-38
    DOI: 10.1016/j.chaos.2013.05.008
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    1. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    2. Bischi, Gian Italo & Lamantia, Fabio, 2007. "Harvesting dynamics in protected and unprotected areas," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 348-370, March.
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    Cited by:

    1. Ziyad AlSharawi & Asma Al-Ghassani & A. M. Amleh, 2015. "Basin of Attraction through Invariant Curves and Dominant Functions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-11, May.
    2. Zhang, Limin & Zhang, Chaofeng & Zhao, Min, 2014. "Dynamic complexities in a discrete predator–prey system with lower critical point for the prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 119-131.

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