BIFURCATION ANALYSIS FOR AROWANA FISH MODEL WITH HARVESTING EFFECT
DOI:
https://doi.org/10.46754/jmsi.2024.06.001Keywords:
Mathematical model, Bifurcation analysis, Arowana fish, Prey-predator, HarvestingAbstract
Wild Asian arowana fish has been an endangered species since 1976 as we need to pay attention to this species to avoid its extinction by chance. Factors that threaten the population of wild arowana fish included its own reproductive method and spawning location. This research is aimed to consider a mathematical model of wild Arowana fish with its prey to easily understand the dynamics of both populations. The model is analyzed both analytically and numerically. We solved the model to obtain equilibria and analyse the stability of equilibria by determining the eigenvalues of Jacobian Matrix of the model considered. The bifurcation analysis was also performed, in which the harvesting rate has been chosen as critical parameter. The results proves that three equilibrium points were found, and the stability condition of these equilibria was analysed. It also turns out that the model undergoes a transcritical bifurcation. Time series and phase portrait were also plotted to see the changes of dynamics for both population for different values of harvesting parameter. Thus, this research is important to educate and increase awareness among human to control their fishing behaviour so that arowana population can be sustained in the future.
References
Danubrata, E. (2009, June 15). Many Asians count on their pet fish for good luck. Reuters. Accessed by 20 January 2023 from https://www.reuters.com/article/us-asia-fishidUSTRE55E1NT20090615
Adams, C. (2024). Arowana care: A complete guide on types, tank setup, diet and more. ModestFish. Accessed by 20 January 2023 from https://modestfish.com/Arowana/
Medipally, S. R., Yusoff, F. M., Sharifhuddin, N., & Shariff, M. (2016). Sustainable aquaculture of Asian Arowana–A review, Journal of Environmental Biology, 37(4), 829-838.
Esmaeili, C., Heng, L. Y., Chiang, C. P., Rashid, Z. A., Safitri, E., & Marugan, R. S. P. M. (2017). A DNA biosensor based on kappa-carrageenan-polypyrrole-gold nanoparticles composite for gender determination of Arowana fish (Scleropages formosus). Sensors and Actuators B: Chemical, 242, 616-624. https://doi.org/10.1016/j.snb.2016.11.061 DOI: https://doi.org/10.1016/j.snb.2016.11.061
de Bello Cioffi, M., Ráb, P., Ezaz, T., Antonio Carlos Bertollo, L., Lavoué, S., Aguiar de Oliveira, E., Sember, A., Franco Molina, W., Henrique Santos de Souza, F., Majtánová, Z., & Liehr, T. (2019). Deciphering the evolutionary history of Arowana fishes (Teleostei, Osteoglossiformes, Osteoglossidae): Insight from comparative cytogenomics. International Journal of Molecular Sciences, 20(17), 4296. DOI: https://doi.org/10.3390/ijms20174296
Yue, G. H., Chang, A., Yuzer, A., & Suwanto, A., (2020). Current knowledge on the biology and aquaculture of the endangered Asian Arowana. Reviews in Fisheries Science & Aquaculture, 28(2), 193-210. DOI: https://doi.org/10.1080/23308249.2019.1697641
Zhang, R., Sun, J., & Yang, H. (2007). Analysis of a prey-predator fishery model with prey reserve. Applied Mathematical Sciences, 1(50), 2481-2492.
Lv, Y., Yuan, R., & Pei, Y. (2013). A prey-predator model with harvesting for fishery resource with reserve area. Applied Mathematical Modelling, 37(5), 3048-3062. https://doi.org/10.1016/J.APM.2012.07.030. DOI: https://doi.org/10.1016/j.apm.2012.07.030
Triharyuni, S., & Aisyah (2018). Predator-prey model of exploited fish population Arowana (Scleropages spp.). IOP Conference Series: Earth and Environmental Science, 176(1), 012037. https://doi.org/10.1088/1755-1315/176/1/012037 DOI: https://doi.org/10.1088/1755-1315/176/1/012037
Belkhodja, K., Moussaoui, A., & Aziz Alaoui, M. A. (2018). Optimal harvesting and stability for a prey-predator model. Nonlinear Analysis: Real World Applications, 39, 321-336. DOI: https://doi.org/10.1016/j.nonrwa.2017.07.004
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. DOI: https://doi.org/10.1016/j.amc.2017.08.052
Raymond, C., Hugo, A., & Kung’aro, M. (2019). Modeling dynamics of prey-predator fishery model with harvesting: A bioeconomic model. Journal of Applied Mathematics, 2019, 1-19. DOI: https://doi.org/10.1155/2019/2601648
Laham, M. F., Krishnarajah, I. S., & Mohd Shariff, J. (2012). Fish harvesting management strategies using logistic growth model. Sains Malaysiana, 41(2), 171-177.
Kot, M. (2001). Elements of mathematical ecology. UK: Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511608520
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