Dynamics of Intra-guild Predation Model with Stage Structure in Prey
DOI:
https://doi.org/10.20956/j.v18i1.14362Keywords:
Intra-guild Predation, Stage Structure, Holling Type I, Beddington-DeAngelisAbstract
The Intra-guild predation model is an interaction between three species where two of them compete and prey on each other for the same resource. This study considers the stage structure of prey on and combines Beddington-DeAngelis and Holling type I as functional responses in the model. Furthermore, the equilibrium point and stability of the model will be analyzed. The numerical result at the equilibrium point shows that the solution converging toward the equilibrium point so that the population is stable and will not become extinct with increasing time. In addition, the population tends to be stable when the density of prey is larger than the predator.
References
Agus, A., Toaha, S. & Kasbawati. 2018. Analisis Model Populasi Mangsa Pemangsa dengan Area Reservasi dan Pemanenan Pemangsa. Jurnal Matematika, Statistika dan Komputasi, Vol. 15, No. 1, 1-12.
Collera, J. A. 2016. Harvesting in Delayed Food Web Model with Omnivory. AIP Conference Proceedings 1705, 020033.
Collera, J.A., & Magpantay, F.M.G. 2018. Dynamics of a Stage Structured Intraguild Predation Model. Springer International Publishing, pp.327-337.
Dubey, B., & Kumar, A. 2019. Dynamics of Prey-Predator Model with Stage Structure in Prey Including Maturation and Gestation Delays. Nonlinear Dynamics.
Han, R., Dai, B., & Wang, Lin. 2018. Delay Induced Spatiotemporal Patterns in a Diffusive Intraguild Predation Model with Beddington-DeAngelis Functional Response. Mathematical Bioscience and Engineering, 595-627.
Garain, K., Kumar, U., & Mandal, P.S. 2019. Global Dynamics in a Beddington-DeAngelis Prey-Predator Model with Density Dependent Death Rate of Predator. Differential Equations and Dynamical Systems, 29.265-283.
Holt, R.D., & Polis, G.A., 1997. A Theoretical Framework for Intraguild Predation. The American Naturalist, 149, 745-764.
Kang, Y., & Wedekin, L. 2013. Dynamic of a Intraguild Predation Model with Generalist or Specialist Predator. Journal of Mathematical Biology, 67(5), 1227-1259.
Pratama, R.A., Toaha, S. & Kasbawati. 2019. Optimal Harvesting ans Stability of Predaror Prey Model with Monod-Haldane Predation Response Function and Stage Structure for Predator. IOP Conference Series: Earth and Environmental Science 279 (1), 012015.
Russel, J.C., Lecomte, V., Dumont, Y., & Corre, M.L. 2009. Intraguild Predation and Mesopredator Release Effect on Long-Lived Prey. Ecological Modelling, 220. 1098-1104
Ringler, D., Russell, J.C., & Corre, M.L. 2015. Trophic Role of Black Rats and Seabird Impacts on Tropical Island: Mesopredator Release or Hyperpredation. Biological Conservation, 185. 75-84.
Siddik, A.M.A., Toaha, S., & Anwar, A.M. 2021. Stability Analysis of Prey-Predator Model with Holling Type IV Functional Response and Infectious Predator. Jurnal Matematika, Statistika dan Komputasi, Vol. 17, No. 2, 155-165.
Toaha, S. Pemodelan Matematika dalam Dinamika Populasi. Makassar, Satu Dua Press, 2013.
Toaha, S., & Azis, M. I. 2018. Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model. IOP Conf. Series: Journal of Physics (Vol. 979). https://doi.org/doi:10.1088/1742-6596/979/1/012069.
7Toaha, S. 2019. The effect of Harvesting with Threshold on the Dynamics of Prey Predator Model. IOP Conf. Series: Journal of Physics 1341 (6), 062021.
Ulya, F.H, Toaha, S. & Kasbawati. 2019. Analisis Kestabilan dan Kontrol Optimal Model Leslie-Gower Fungsi Respon Holling III dengan Pemanenan pada Populasi Predator dan Prey. Jurnal Matematika, Statistika dan Komputasi. Vol 16, Nol 1, 74-87. doi:10.20956/jmsk.v16i1.6784.
Wei, H. C., Chen, Y. Y., Lin, J. T., & Hwang, S. F. 2018. The Dynamics of an Intraguild Predation Model with Prey Switching. AIP Conference Proceedings 1978, 470012.
Widihastuty. 2010. Predasi Intraguild: Fenomena dan Pengaruhnya dalam Pengendalian Hayati. Kopertis Wilayah Nanggroe Aceh Darussalam (NAD), Sumatra Utara, Indonesia. Vol. 14. No.2.
Yusrianto, Y., Toaha, S. & Kasbawati. 2019. Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa. Jurnal Matematika, Statistika dan Komputasi, Vol. 16, No. 1, 97-106.
Zhang, D & Dai, B. 2018. Spreading and Vanishing in a Diffusive Intraguild Predation Model with Intraspecific Competition and Free Boundary. Mathematical Method Applied Sciences, 42.1-27
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