Stability Analysis of Fixed Points in Forest Biomass Depletion Model
DOI:
https://doi.org/10.31958/js.v15i2.9240Keywords:
Fixed points, Forest biomass, Population, Stability.Abstract
The main focus of this article is to present a model that explains the depletion in forest biomass  due to population size , population pressure , and industrialization . This research explores the complex relationship between forest biomass, population growth, and industrialization. The model generates four fixed points that are all non-negative, and they are known as and . The article proceeds to analyze the stability of these fixed points in the context of forest biomass depletion. It is discovered that the fixed points  and are saddle points and not stable, while the fixed point  is stable if it meets certain conditions. The article concludes by carrying out numerical simulations to determine the equilibrium point of the model, which shows that forest resource biomass stability declines as population size, population pressure, and industrialization increase. The simulations reveal that population growth results in a depletion in forest resource biomass, while the opposite is true for the positive impact that forest resource biomass on population levels. Consequently, it is essential to regulate population density and industrialization to manage population growth and protect forest resources.References
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Wakhidah, U. U. S., Nugraheni, K., & Winarni, W. (2022). Analysis of Mangrove Forest Resource Depletion Models due to The Opening of Fish Pond Land with Time Delay. Jurnal ILMU DASAR, 23(1), 65. https://doi.org/10.19184/jid.v23i1.23889
Boyce, W. E., & DiPrima, R. E. (2012). Elementary Differential Equation and Boundary Value Problems.
Dubey, B., Sharma, S., Sinha, P., & Shukla, J. B. (2009). Modelling the depletion of forestry resources by population and population pressure augmented industrialization. Applied Mathematical Modelling, 33(7), 3002–3014. https://doi.org/10.1016/j.apm.2008.10.028
Dubey, B., Upadhyay, R. K., & Hussain, J. (2002). Effects of industrialization and pollution on resource biomass: A mathematical model. In Ecological Modelling (Issues 1–2). https://doi.org/10.1016/S0304-3800(03)00168-6
Khalil, H. K. (2002). Nonlinear Systems. In Upper Saddle River. NJ: Prentice Hall.
Mohamad, R., Rauf, M. D. A., & Lakisa, N. (2019). Model Matematika Kerusakan Hutan dengan Memperhatikan Faktor Industri dan Kebakaran. EULER: Jurnal Matematika, Sains Dan Teknologi, 7(1), 6–14.
Ramdhani, V., Jaharuddin, & Nugrahani, E. H. (2015). Dynamical system of modelling the depletion of forestry resources due to crowding by industrialization. Applied Mathematical Sciences, 9(81–84), 4067–4079. https://doi.org/10.12988/ams.2015.53259
Robinson, J. (2004). An Introduction to Ordinary Differential Equations.UK: Cambridge University Press.
Shukla, J. B., Kusum, L., & Misra, A. K. (2011). Resource By Population and Industrialization : Effect of Technology on Its Conservation. Natural Resource Modeling, 24(2), 242–267.
Sundar, S., Swaroop, N., & Naresh, R. (2017). Modeling the Effect of Population and Population Augmented Industrialization on Forestry Resources. European Journal of Engineering Research and Science, 2(1), 65. https://doi.org/10.24018/ejers.2017.2.1.247
Wakhidah, U. U. S., Nugraheni, K., & Winarni, W. (2022). Analysis of Mangrove Forest Resource Depletion Models due to The Opening of Fish Pond Land with Time Delay. Jurnal ILMU DASAR, 23(1), 65. https://doi.org/10.19184/jid.v23i1.23889
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2023-12-31
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