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Hengki Tasman
Department Of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
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Pendekatan Geometris untuk Model Predator-Prey dengan Carrying Capacity pada Populasi Prey Marshellino; Tasman, Hengki; Rusin, Rahmi
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.2.1

Abstract

In this paper, we explore a classical predator-prey model where the birth rate of the prey is significantly lower than the mortality rate of the predators, while also considering a limited prey population. We incorporate an environmental carrying capacity factor for the prey to account for this. Given the different timescales of the predator and prey populations, some system solutions may exhibit a fast-slow structure. We analyze this fastslow behavior using geometric singular perturbation theory (GSPT), which allows us to separate the system into fast and slow subsystems. Our research investigates the existence and stability of equilibrium solutions and the behavior of solutions near the critical manifold. Additionally, we use an entry-exit function to analytically establish the connection between the solutions of the slow subsystem and those of the fast subsystem.
Co-Authors Adang Suwandi Ahmad Adi Pancoro Arthana Islamilova Bevina D Handari Dewi Putrie Lestari Dipo Aldila Edy Soewono Filla, M. Shiqo John, Peter Jorga Ibrahim Marshellino Mohammad Bahrelfi Belatiff Muhammad Sukrisno Mardiyanto Nicola Chandra Darmawan Nova Meyana Sabara Nova Sabara Ria Lestari Moedomo Rusin, Rahmi Sarbaz H.A. Khosnaw Theo Tuwankotta Wono Setya Budhi