E3S Web Conf.
Volume 73, 2018The 3rd International Conference on Energy, Environmental and Information System (ICENIS 2018)
|Number of page(s)||3|
|Section||Environmental Health, Toxicology and Epidemiology|
|Published online||21 December 2018|
Analysis of a Prey-Predator Fishing Model for Harvesting with The Limited Effect of Density and Toxicity
Departement of Mathematics, Faculty of Sciences and Mathematics, Universitas Diponegoro, Semarang, Indonesia
* Corresponding author: dita.aniesfgjundip.ac. id
We proposed a model of prey-predator fishing by considering proportion of prey density and toxicity in ecosystem. The model is analysed to study about biological equilibrium, bionomic equilibrium and its stability. The aim of the model is to determine the optimal sustainable harvesting for each species. The optimal harvesting is resulted from Pontryagin’s maximal principle. The global stability of coexistence equilibrium is analyzed from Lyapunov function. The effect of toxicity leads to the decreasing of sustainable harvesting.
Key words: Prey-predator / harvesting / equilibrium / stability
© 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.
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