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DIAN SAVITRI
Department of Child Health, Udayana University Medical School/Sanglah Hospital Denpasar
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Journal : Jurnal Matematika UNAND

 1 
UNRAVELING THE IMPACT OF THE MEMORY, THE COMPETITION, AND THE LINEAR HARVESTING ON A LOTKA-VOLTERRA MODEL PANIGORO, HASAN S.; RAHMI, EMLI; SAVITRI, DIAN; BEAY, LAZARUS KALVEIN
Jurnal Matematika UNAND Vol 13, No 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.257-269.2024

Abstract

The harvesting of population has a dominant influence in balancing the ecosystem. In this manuscript, the impact of harvesting in addition to competition, and memory effect on a prey-predator interaction following the Lotka-Volterra model is studied. The mathematical validation is provided by proofing that all solutions of the model are always exist, non-negative, and bounded. Obeying Matignon condition, Lyapunov function, and generalized LaSalle invariance principle, the local and global stability are investigated. To complete the analytical results, some numerical simulations are given to show the occurrence of forward bifurcation and the impact of the memory index. All results state that three possible circumstances may occur namely the extinction of both populations, the prey-only population, and the co-existence of both populations.
UNRAVELING THE IMPACT OF THE MEMORY, THE COMPETITION, AND THE LINEAR HARVESTING ON A LOTKA-VOLTERRA MODEL PANIGORO, HASAN S.; RAHMI, EMLI; SAVITRI, DIAN; BEAY, LAZARUS KALVEIN
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.257-269.2024

Abstract

The harvesting of population has a dominant influence in balancing the ecosystem. In this manuscript, the impact of harvesting in addition to competition, and memory effect on a prey-predator interaction following the Lotka-Volterra model is studied. The mathematical validation is provided by proofing that all solutions of the model are always exist, non-negative, and bounded. Obeying Matignon condition, Lyapunov function, and generalized LaSalle invariance principle, the local and global stability are investigated. To complete the analytical results, some numerical simulations are given to show the occurrence of forward bifurcation and the impact of the memory index. All results state that three possible circumstances may occur namely the extinction of both populations, the prey-only population, and the co-existence of both populations.
Co-Authors ABADI Akmal Ali, Muhamad Restu Alya, Aiza Andreani, Phobe APRILIA, VERNANDA Beay, Lazarus Kalvein BUDI RAHADJENG Danu Erlangga, Muhammad Dewi, Mifta Kharisma Dina Kartika Maharani DINA KARTIKA MAHARANI Dini Kinati Fardah Dino, Awan Eghary, Nabila Kholifatul Yuniar Faradilla, Anisa' Fitri, Davina Alma Gastriani, Ovi Prina Hamzah, Ahmad Taufik Hasan S. Panigoro Hidajati, Ninik Wahju I Made Kardana Isaloka, Ilo Jakfar, Muhammad Khofifah, Rike Farikha Kusumawati Dwiningsih Lydia Rohmawati Mahameru Rosy Rochmatullah Manuharawati Meladelvia, Nabilah Ni Putu Siadi Purniti Ninuk Lustyantie Nisa', Anastasya Choirun Phibeta, Toni Prawoto, Budi P. Putri, Laras Kinanti RADEN SULAIMAN Rahmi, Emli Ratna Salsabila, An Nisa Salsabillah, Atiyah Safitri Sri Harini Ekowati Sri Mulyani Subur Ismail, Subur Thoriq, Abil Alfath Umaroh, Siti Zulfaniah Wiediartini Wiediartini