The impact of constant effort harvesting on the dynamics of a discrete‐time contest competition model

Abstract

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 equationthe 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.

High codimension bifurcations analysis in a predator-prey system with Michaelis-Menten type predator harvesting

“…To solve this problem, harvesting terms were added to the predator-prey model. Depending on the type of harvesting [19,20,42], there are three types of harvesting: constant-yield harvesting [28,30,39], constant-effort harvesting [1,6], and nonlinear type harvesting [2,10,11,13,37,45], such as Michaelis-Menten type harvesting [16]. Nonlinear type harvesting has a functional relationship of Holling II type with the current number of harvested biological populations and human effort, which has a certain saturation effect on the current number of biological populations and human effort.…”