Application of Beddington DeAngelis Response Function in Ecological Mathematical System: Study Fish Endemic Oliv Predator Species in Merauke

Rian Ade Pratama; Maria Fransina Veronica Ruslau

doi:10.31764/jtam.v6i1.5340

Application of Beddington DeAngelis Response Function in Ecological Mathematical System: Study Fish Endemic Oliv Predator Species in Merauke

Rian Ade Pratama, Maria Fransina Veronica Ruslau

Abstract

Predator-prey type fishery models Oliv fish is a trans-endemic predator species that inhabits freshwater swamps and brackish water in Merauke, Papua. Maintaining the survival of the Oliv fish species is the main reason for compiling a mathematical model, so that it can be considered by local governments in making ecological policies. Method on model discussed is assembled with the growth of predator-prey populations following the growth of logistics. The response or predatory function corresponding to the behavior of endemic Oliv fish is the Beddington DeAngelis type. The growth of predatory species uses the concept of growth with stage structure, are divided into mature and immature. Research results show there are four equilibrium points of the mathematical model, but only one point becomes the asymptotic stable equilibrium point without harvesting W_4 (x^*,y^*,z^* )=92.823,1311.489,525.957 and equilibrium point with harvesting W_4 (x^*,y^*,z^* )=95.062,92.639,160.466 . Harvesting exploitation efforts are carried out by the community so that the harvesting variables are added with a proportional concept. Simulation of the results of the study shows a stable scheme and harvesting conducted can maintain the number of populations that continue.

Keywords

Predator-prey; Beddington DeAngelis; Harvesting;

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References

Ang, T. K., & Safuan, H. M. (2019). Harvesting in a toxicated intraguild predator–prey fishery model with variable carrying capacity. Chaos, Solitons and Fractals, 126, 158–168. https://doi.org/10.1016/j.chaos.2019.06.004

Belkhodja, K., Moussaoui, A., & Alaoui, M. A. A. (2018). Optimal harvesting and stability for a prey–predator model. Nonlinear Analysis: Real World Applications, 39, 321–336. https://doi.org/10.1016/j.nonrwa.2017.07.004

Chakraborty, K., Das, S., & Kar, T. K. (2013). On non-selective harvesting of a multispecies fishery incorporating partial closure for the populations. Applied Mathematics and Computation, 221, 581–597. https://doi.org/10.1016/j.amc.2013.06.065

Datta, J., Jana, D., & Upadhyay, R. K. (2019). Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting. Chaos, Solitons and Fractals, 122, 229–235. https://doi.org/10.1016/j.chaos.2019.02.010

Ghanbari, B., Günerhan, H., & Srivastava, H. M. (2020). An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model. Chaos, Solitons and Fractals, 138, 109910. https://doi.org/10.1016/j.chaos.2020.109910

Ghosh, B., Zhdanova, O. L., Barman, B., & Frisman, E. Y. (2020). Dynamics of stage-structure predator-prey systems under density-dependent effect and mortality. Ecological Complexity, 41(December 2019), 100812. https://doi.org/10.1016/j.ecocom.2020.100812

Jia, Y., Li, Y., & Wu, J. (2017). Effect of predator cannibalism and prey growth on the dynamic behavior for a predator-stage structured population model with diffusion. Journal of Mathematical Analysis and Applications, 449(2), 1479–1501. https://doi.org/10.1016/j.jmaa.2016.12.036

Kaushik, R., & Banerjee, S. (2021). Predator-prey system: Prey’s counter-attack on juvenile predators shows opposite side of the same ecological coin. Applied Mathematics and Computation, 388, 125530. https://doi.org/10.1016/j.amc.2020.125530

Kundu, S., & Maitra, S. (2018). Dynamics of a delayed predator-prey system with stage structure and cooperation for preys. Chaos, Solitons and Fractals, 114, 453–460. https://doi.org/10.1016/j.chaos.2018.07.013

Li, M., Chen, B., & Ye, H. (2017). A bioeconomic differential algebraic predator–prey model with nonlinear prey harvesting. Applied Mathematical Modelling, 42, 17–28. https://doi.org/10.1016/j.apm.2016.09.029

Liu, X., & Huang, Q. (2020). Analysis of optimal harvesting of a predator-prey model with Holling type IV functional response. Ecological Complexity, 42(October 2019), 100816. https://doi.org/10.1016/j.ecocom.2020.100816

Lu, Y., Pawelek, K. A., & Liu, S. (2017). A stage-structured predator-prey model with predation over juvenile prey. Applied Mathematics and Computation, 297, 115–130. https://doi.org/10.1016/j.amc.2016.10.035

Malard, J., Adamowski, J., Nassar, J. B., Anandaraja, N., Tuy, H., & Melgar-Quiñonez, H. (2020). Modelling predation: Theoretical criteria and empirical evaluation of functional form equations for predator-prey systems. Ecological Modelling, 437(June), 109264. https://doi.org/10.1016/j.ecolmodel.2020.109264

Manna, D., Maiti, A., & Samanta, G. P. (2018). Analysis of a predator-prey model for exploited fish populations with schooling behavior. Applied Mathematics and Computation, 317, 35–48. https://doi.org/10.1016/j.amc.2017.08.052

Pratama, R. A., Ruslau, M. F. V., & Nurhayati. (2021). Global Analysis of Stage Structure Two Predators Two Prey Systems under Harvesting Effect for Mature Predators. Journal of Physics: Conference Series, 1899(1). https://doi.org/10.1088/1742-6596/1899/1/012099

Pratama, R. A., Toaha, S., & Kasbawati. (2019). Optimal harvesting and stability of predator prey model with Monod-Haldane predation response function and stage structure for predator. IOP Conference Series: Earth and Environmental Science, 279(1). https://doi.org/10.1088/1755-1315/279/1/012015

Vijaya Lakshmi, G. M. (2020). Effect of herd behaviour prey-predator model with competition in predator. Materials Today: Proceedings, 33(xxxx), 3197–3200. https://doi.org/10.1016/j.matpr.2020.04.166

Walters, C., Christensen, V., Fulton, B., Smith, A. D. M., & Hilborn, R. (2016). Predictions from simple predator-prey theory about impacts of harvesting forage fishes. Ecological Modelling, 337, 272–280. https://doi.org/10.1016/j.ecolmodel.2016.07.014

Wang, X., & Huang, C. (2014). Permanence of a stage-structured predator-prey system with impulsive stocking prey and harvesting predator. Applied Mathematics and Computation, 235, 32–42. https://doi.org/10.1016/j.amc.2014.02.092

Yanni, M. H., & Zulfahmi. (2019). Analisis Pemodelan dan Simulasi Matematika Pengendalian Epidemi Toksoplasmosis. JTAM (Jurnal Teori Dan Aplikasi Matematika), 3(2), 114–120.

Yulida, Y., & Karim, M. A. (2019). Analisa Kestabilan dan Solusi Pendekatan Pada Persamaan Van der Pol. JTAM | Jurnal Teori Dan Aplikasi Matematika, 3(2), 156. https://doi.org/10.31764/jtam.v3i2.1084

Zhao, X., & Zeng, Z. (2019). Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator. Physica A. https://doi.org/10.1016/j.physa.2019.123310

DOI: https://doi.org/10.31764/jtam.v6i1.5340