Now showing 1 - 4 of 4
  • Publication
    Basin of Attraction through Invariant Curves and Dominant Functions
    (Hindawi Publishing Corporation, 2015)
    Alsharawi, Z.
    ;
    Al-Ghassani, A.
    ;
    We study a second-order difference equation of the form zn+1 = zn F (zn-1) + h, where both F (z) and z F (z) are decreasing. We consider a set of invariant curves at h = 1 and use it to characterize the behaviour of solutions when h > 1 and when 0 < h < 1. The case h > 1 is related to the Y2K problem. For 0 < h < 1, we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria. © 2015 Ziyad AlSharawi et al.
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  • Publication
    Eventual Monotonicity in Nonlinear Difference Equations
    (2016) ;
    Drymonis, Emmanouil
    This paper continues our study on the global character of solutions of a certain rational difference equation. We present several new results together with some known techniques which establish the eventually monotonic character of solutions for a class of nonlinear difference equations in a certain range of their parameters. Open problems and conjectures are provided for further investigations.
      66
  • Publication
    Harvesting and stocking in discrete-time contest competition models with open problems and conjectures
    (2016) ;
    Alsharawi, Ziyad
    In this survey, we present a class of first and second-order difference equations rep-resenting general form of discrete models arising from single-species with contest competition. Then, we consider various harvesting/stocking strategies and discuss their effect on stability, persistence and maximum sustainable yield. The main aim of this work is to give an account of recent results on the subject within a unified framework, then present some open questions and conjectures that deserve further investigation.
      67  55
  • Publication
    The impact of constant effort harvesting on the dynamics of a discrete-time contest competition model
    (John Wiley and Sons Ltd, 2017) ;
    Alsharawi, Ziyad
    In this paper, we study a general discrete-time model representing the dynamics of a contest competition species with constant effort exploitation. In particular, we consider the difference equation xn+1=xnf(xn-k)-hxn where h>0, k∈(0,1), and the density dependent function f satisfies certain conditions that are typical of a contest competition. The harvesting parameter h is considered as the main parameter, and its effect on the general dynamics of the model is investigated. In the absence of delay in the recruitment (k=0), we show the effect of h on the stability, the maximum sustainable yield, the persistence of solutions, and how the intraspecific competition change from contest to scramble competition. When the delay in recruitment is 1 (k=1), we show that a Neimark-Sacker bifurcation occurs, and the obtained invariant curve is supercritical. Furthermore, we give a characterization of the persistent set. © 2017 John Wiley & Sons, Ltd.
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