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Journal of Applied Nonlinear Dynamics 11(4) (2022) 817--832 | DOI:10.5890/JAND.2022.12.004

S.M. Mahathy Hasan$^1$, Md. Haider Ali Biswas$^1$, Laek Sazzad Andallah$^2$

$^1$ Department of Mathematics, Jahangirnagar University, Saver, Dhaka, Bangladesh

$^2$ Mathematics Discipline, khulna University, Khulna, Bangladesh

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Abstract

In this paper, we consider two competing fish population which are subject to be harvested. The growth of them follows the logistic growth function. From different sources release toxic substances which are harmful to each fish species. The boundedness equilibria, stability, bionomic equilibrium, optimal harvesting policy and optimal control have been studied. We have shown that the dynamical outcomes of the interacting fish species will much sensitive to the system parameters and their initial population volumes. Counter-intuitive results on role played by toxic coefficients are highly gated. Finally, some numerical example are cited to illustrate the effect of toxicity upon the species and optimal control theory is applied to minimize the harmful toxic effect

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