TY - JOUR
T1 - The impact of constant effort harvesting on the dynamics of a discrete-time contest competition model
AU - Alsharawi, Ziyad
AU - Amleh, Amal
N1 - Funding Information:
The first author is partially supported by a seed grant offered by the American University of Sharjah.
Publisher Copyright:
© 2017 John Wiley & Sons, Ltd.
PY - 2017/12
Y1 - 2017/12
N2 - 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 = xn f(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.
AB - 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 = xn f(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.
KW - Contest competition
KW - Neimark-Sacker bifurcation
KW - Persistence
KW - Scramble competition
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U2 - 10.1002/mma.4487
DO - 10.1002/mma.4487
M3 - Article
AN - SCOPUS:85022321659
SN - 0170-4214
VL - 40
SP - 6747
EP - 6759
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 18
ER -