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The impact of constant effort harvesting on the dynamics of a discrete-time contest competition model. (English) Zbl 1382.92213
Summary: 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 \(x_{n+1}=x_{n}f(x_{n-k})-hx_{n}\) where \(h>0\), \(k\in \{0,1\}\), 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.
92D25 Population dynamics (general)
39A10 Additive difference equations
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