Hopf bifurcation in a dynamic mathematical model in facultative waste stabilization pond

Authors

  • GESTI ESSA WALDHANI WALDHANI Jurusan Teknologi Informasi, Fakultas Teknologi Informasi, Universitas Bina Sarana Informatika, Jakarta, Indonesia

DOI:

https://doi.org/10.20956/j.v21i2.41888

Keywords:

Hopf bifurcation, dynamic mathematical model, stabilization pond

Abstract

 In this paper, we discuss the predator-prey model using Holling type II functional response with the time delay in facultative stabilization pond. In this research, we discuss the predator-prey model using Holling type II functional response with the time delay, determining the equilibrium point, the stability analysis of predator-prey model using Holling type II functional response with the time delay and numerical simulation of the predator-prey model using Holling type II functional response with the time delay. The method used to analyse the problem is by literature study. The steps used are the development of a mathematical model of change of dissolved oxygen concentration, phytoplankton and zooplankton, mathematical equation solving algorithm, field data, simulation using Maple and Mathematica 9 software and validation with research.

References

[1] Anton, H., 2005. Elementary Linear Algebra 9th Edition. Singapore: John Wiley &Sons.

[2] Clark, D. N., 1999. Analysis Calculus and Differential Equation. New York: CRC Press.

[3] Clark, D. N. 2000. Dictionary of Analysis, Calculus and Differential Equations. New York: CRC Press, Boca Raton.

[4] Hull, V., 2008. Modelling dissolved oxygen dynamics in coastal lagoons. Ecological Modelling, Vol. 211, 468–480.

[5] Irwan, 2009. Dynamic Behavior of Competition System Between Tumors with Immune in Delay Differential Equations. Department of Mathematics ITS.

[6] Liao, X. et al., 2007. Stability of Dynamical Systems. Elsevier, Vol. 5.

[7] Misra, A. K, 2010. Modeling the depletion of dissolved oxygen in a lake due to submerged macrophytes. Nonlinear Analalysis Modelling and Control, Vol. 15, No. 2, 185– 198.

[8] Misra, A. K. et al., 2011. Modeling the depletion of dissolved oxygen in a lake due to algal bloom: Effect of time delay. Advances in Water Resources, Vol. 34, No. 12, 1232–1238.

[9] Olsder, G. J. et al., 2004 Mathematical System Theory. Netherlands: VVSD.

[10] Strogatz, S. H. 2014. Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering Second Edition. Massachusetts: Cambridge Perseus Books.

[11] Sekerci, Y., Petrovskii, S., 2015. Mathematical Modelling of Plankton–Oxygen Dynamics Under the Climate Change. Bull Math Biol, Vol. 77, No. 12, 2325–2353.

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Published

2025-01-12

How to Cite

WALDHANI, G. E. W. (2025). Hopf bifurcation in a dynamic mathematical model in facultative waste stabilization pond. Jurnal Matematika, Statistika Dan Komputasi, 21(2), 544–559. https://doi.org/10.20956/j.v21i2.41888

Issue

Section

Research Articles