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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.
##### MSC:
 92D25 Population dynamics (general) 39A10 Additive difference equations
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