ANALYSIS DINAMIC AND BIOECONOMIC OF A PREDATOR-PREY SYSTEM WITH MARINE NATIONAL PARK

Rian Ade Pratama* -  Universitas Musamus, Indonesia
Candra Agus Wahyudi -  Universitas Musamus, Indonesia

DOI : 10.24269/silogisme.v8i1.6771

In the study of fisheries or marine products in developing countries, the problem of managing marine resources is often faced. Excessive exploitation due to weak legal and supervisory sectors is the most frequently used factor. This research involves a predator-prey mathematical model and provides an intervention variable exploitation, namely harvest. Harvest is carried out on two types of species that inhabit two protected areas of the marine national park zone. One of the objectives of the exploitation variable is to provide benefits for harvesters, such as fishermen. Boundary areas in the marine national park zone and points of equilibrium are assigned to research wetting. Stability analysis using the Routh-Hurwitz criteria indicates the survival of the population. The predator-prey model formed resulted in seven non-negative equilibria, but only one equilibrium point met the research assumptions. Numerical simulations are also provided in trajectories from the initial model formation to the bionomic shape. The basic assumption is that harvesting is carried out in the marine national park zone harvesting is carried out only in a limited way. In the prey one population, more can be harvested in the region than the prey two population. Ecologically, the population of prey one lives in a larger carrying capacity area. In the predator-prey model system, the predator-prey model makes it possible to harvest populations that live in a wider area. The wider the area of the marine national park zone, the more it is permitted to carry out exploitation efforts, provided that it is still limited.

Supplement Files

Keywords
Bionomic, Predator-Prey, Marine National Park.
  1. 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
  2. Chakraborty, K., Chakraborty, M., & Kar, T. K. (2011). Bifurcation and control of a bioeconomic model of a prey-predator system with a time delay. Nonlinear Analysis: Hybrid Systems, 5(4), 613–625. https://doi.org/10.1016/j.nahs.2011.05.004
  3. Das, U., Kar, T. K., & Pahari, U. K. (2013). Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge. ISRN Biomathematics, 2013, 1–12. https://doi.org/10.1155/2013/637640
  4. Fajarningsih, N. D., Januar, H. I., Nursid, M., & Wikanta, T. (2006). Potensi Antitumor Ekstrak Spons Crella papilata Asal Taman Nasional Laut Kepulauan Seribu. Jurnal Pascapanen Dan Bioteknologi Kelautan Dan Perikanan, 1(1), 35. https://doi.org/10.15578/jpbkp.v1i1.229
  5. Iskandar, A., Muslim, M., Hendriana, A., & Wiyoto, W. (2021). Jenis-Jenis Ikan Indonesia yang Kritis dan Terancam Punah. Jurnal Sains Terapan, 10(1), 53–59. https://doi.org/10.29244/jstsv.10.1.53-59
  6. Islamiyati, A. (2019). Regresi Spline Polynomial Truncated Biprediktor untuk Identifikasi Perubahan Jumlah Trombosit Pasien Demam Berdarah Dengue. Al-Khwarizmi: Jurnal Pendidikan Matematika Dan Ilmu Pengetahuan Alam, 7(2), 97–112. https://doi.org/10.24256/jpmipa.v7i2.799
  7. Jimmi, Riani, E., & Affandi, R. (2011). Keanekaragaman Dan Kelimpahan Ikan Kerapu ( Serranidae ) Di Daerah Reservasi ( Zona Inti ) Dan Non-Reservasi ( Zona Pemukiman ) Taman Nasional Laut Kepulauan Seribu, Jakarta. Jurnal Ilmu-Ilmu Perairan Dan Perikanan Indonesia, 17(Juni), 245–253.
  8. Kaligis, F., Eisenbarth, J. H., Schillo, D., Dialao, J., Schäberle, T. F., Böhringer, N., Bara, R., Reumschüssel, S., König, G. M., & Wägele, H. (2018). Second survey of heterobranch sea slugs (Mollusca, Gastropoda, Heterobranchia) from Bunaken National Park, North Sulawesi, Indonesia - How much do we know after 12 years? Marine Biodiversity Records, 11(1), 1–20. https://doi.org/10.1186/s41200-018-0136-3
  9. Kar, T., & Chakraborty, K. (2010). Bioeconomic modelling of a prey predator system using differential algebraic equations. International Journal of Engineering, Science and Technology, 2(1). https://doi.org/10.4314/ijest.v2i1.59081
  10. Khan, A. Q., Ibrahim, T. F., & Khaliq, A. (2021). Stability and Bifurcation Analysis of Discrete Dynamical Systems 2020. Discrete Dynamics in Nature and Society, 2021. https://doi.org/10.1155/2021/9821615
  11. 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
  12. Ling, S. D., & Johnson, C. R. (2012). Marine reserves reduce risk of climate-driven phase shift by reinstating size- and habitat-specific trophic interactions. Ecological Applications, 22(4), 1232–1245. https://doi.org/10.1890/11-1587.1
  13. Micheli, F., Amarasekare, P., Bascompte, J., & Gerber, L. R. (2004). Including species interactions in the design and evaluation of marine reserves: Some insights from a predator-prey model. Bulletin of Marine Science, 74(3), 653–669.
  14. Nasyrah, A. F. A., Rahardjo, M. F., Simanjuntak, C. P. H., & Nur, M. (2021). The length-weight relationships and condition factor of an endemic Marosatherina ladigesi Ahl, 1936 in Walanae Cenranae River Watershed, South Sulawesi, Indonesia . E3S Web of Conferences, 322, 01002. https://doi.org/10.1051/e3sconf/202132201002
  15. Pal, D., & Mahapatra, G. S. (2014). A bioeconomic modeling of two-prey and one-predator fishery model with optimal harvesting policy through hybridization approach. Applied Mathematics and Computation, 242, 748–763. https://doi.org/10.1016/j.amc.2014.06.018
  16. Powell, A., Jones, T., Smith, D. J., Jompa, J., & Bell, J. J. (2015). Spongivory in the Wakatobi Marine National Park, Southeast Sulawesi, Indonesia1. Pacific Science, 69(4), 487–508. https://doi.org/10.2984/69.4.5
  17. Pratama, R. A. (2022). IMPACT OF FEAR BEHAVIOR ON PREY POPULATION GROWTH PREY-PREDATOR INTERACTION. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(2), 371–378.
  18. Sambali, H., Yulianda, F., Bengen, D. G., & Kamal, M. M. (2015). Analisis Kelembagaan Pengelola Taman Nasional Laut Kepulauan Seribu. Jurnal Sosial Ekonomi Kelautan Dan Perikanan, 9(1), 105. https://doi.org/10.15578/jsekp.v9i1.1188
  19. Shang, Z., Qiao, Y., Duan, L., & Miao, J. (2021). Bifurcation analysis in a predator–prey system with an increasing functional response and constant-yield prey harvesting. Mathematics and Computers in Simulation, 190, 976–1002. https://doi.org/10.1016/j.matcom.2021.06.024
  20. Tobing, I. S., Ruslan, H., & Rahayu, S. (2013). Perbedaan Komunitas Arthropoda Tanah Antar Tipe Habitat di Pulau Kotok Besar Taman Nasional Laut Kepulauan Seribu. Prosiding SEMINAR NASIONAL BIOLOGI, May 2018. https://www.researchgate.net/publication/345002066_Prosiding_SEMINAR_NASIONAL_BIOLOGI/link/5f9bead6a6fdccfd7b8a86d0/download
  21. Umar, A., & Musa, S. (2018). A Modified Bioeconomic Model for Prey-Predator Interaction in Polluted Environment with Constant Harvesting: Reserve Zones and Taxation as Combine Control Strategy. July.
  22. Umar, C., & Sulaiman, P. S. (2013). Status Introduksi Ikan Dan Strategi Pelaksanaan Secara Berkelanjutan Di Perairan Umum Daratan Di Indonesia. Jurnal Kebijakan Perikanan Indonesia, 5(2), 113. https://doi.org/10.15578/jkpi.5.2.2013.113-120
  23. Yazici, G., & Bal, N. (2022). Diversity, Ecological Properties of Dipsocoromorpha, Enicocephalomorpha, Gerromorpha, Leptopodomorpha and Nepomorpha (Heteroptera: Hemiptera) in Turkey. Archives of Life Sciences and Nutritional Research Compilation Article, 6(1), 1–13. https://doi.org/10.31829/2765-8368/alsnr2022-6(1)-001
  24. Yokoo, T., Kanou, K., Moteki, M., Kohno, H., Tongnunui, P., & Kurokura, H. (2012). Assemblage structures and spatial distributions of small gobioid fishes in a mangrove estuary, southern Thailand. Fisheries Science, 78(2), 237–247. https://doi.org/10.1007/s12562-011-0447-3
  25. Zhang, Y., Li, N., & Zhang, J. (2019). Stochastic stability and Hopf bifurcation analysis of a singular bio-economic model with stochastic fluctuations. International Journal of Biomathematics, 12(8). https://doi.org/10.1142/S1793524519500839

Full Text: Supp. File(s):
ANALYSIS DINAMIC AND BIOECONOMIC OF A PREDATOR-PREY SYSTEM WITH MARINE NATIONAL PARK
Subject
Type HASIL TURNITIN
  Download (B)    Indexing metadata
Article Info
Submitted: 2023-02-21
Published: 2023-06-08
Section: Artikel
Article Statistics: