E3S Web Conf.
Volume 31, 2018The 2nd International Conference on Energy, Environmental and Information System (ICENIS 2017)
|Number of page(s)||6|
|Section||08. Environmental Conservation|
|Published online||21 February 2018|
Analysis of a Fishery Model with two competing prey species in the presence of a predator species for Optimal Harvesting
Department of Mathematics, Faculty of Sciences and Mathematics, Diponegoro University, Semarang - Indonesia
2 Department of Environmental Engineering, Faculty of Engineering, Diponegoro University, Semarang - Indonesia
* Corresponding author: firstname.lastname@example.org
A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin’s maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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