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Discontinuity, Nonlinearity, and Complexity 13(3) (2024) 483--494 | DOI:10.5890/DNC.2024.09.007

Nurul Huda Gazi$^1$, Ajijur Rahaman Mallick$^2$

$^1$ Aliah University, Department of Mathematics & Statistics, IIA/27, Newtown, Kolkata- 700 160, India

$^2$ Department of Mathematics Maheshtala College, B.B.T. Road, Kolkata- 700139, India

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Abstract

In this paper we have considered a predator-prey system under harvesting. The prey population obey the law of logistic growth. The predator functional response to prey density is taken in such a manner that when prey population increase the predator's functional response tends to a constant value. The predator population are under competition among themselves. The existence of the solution of the nonlinear system are carried out. The steady states and the stability of the system are analyzed. We have tested the stability of the models system at the equilibrium points by using variational method. The existence of bionomic equilibrium has been carried out. The Pontryagin's maximum principle has been used for the analysis of the optimal harvesting policy of the model system.

Acknowledgments

\bibitem{SCFWalker2001} Schefer, M., Carpenter, S., Foley, J.A., Folke, C., and Walker, B. (2001), Catastrophic shifts in ecosystems, \textit{Nature}, \textbf{413}, 591-596.

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