# KONTROL OPTIMAL MODEL LESLIE-GOWER DENGAN PEMANENAN PADA POPULASI PREDATOR DAN PERLINDUNGAN PADA PREY

## (OPTIMAL CONTROL FOR LESLIE-GOWER MODEL WITH HARVESTING ON PREDATOR POPULATIONS AND PROTECTION FOR PREY)

• Moh. Nurul Huda Mulawarman University
• Sri Wigantono Jurursan Matematika, Fakultas MIPA, Universitas Mulawarman
• Syaripuddin Syaripuddin Jurursan Matematika, Fakultas MIPA, Universitas Mulawarman
• Rizal Furqan Ramadhan Jurusan Manajemen Bisnis Syariah,Universitas Islam Negeri Sayyid Ali Rahmatullah

### Abstract

ABSTRACT. This paper studied the Leslie-Gower predator-prey model with the effects of prey refuge and linear harvesting on predator populations. Prey populations grow as a logistic model when there is no interaction with predators. The predator population is assumed to have economic value. Analysis of Bionomic and Harvesting Control have been studied further. The results showed that the protective effect of prey had an effect on harvesting activity in the population so that it affected profits in predatory harvests. Simulation of several calculations is given to purchase the analysis results..
Keywords: Linear harvesting, Leslie-Gower Model, Binomics, prey refuge.

ABSTRAK. Artikel ini membahas model predator-prey Leslie-Gower dengan efek perlindungan prey dan pemanenan linear pada populasi predator. Populasi prey tumbuh sebagai model logistik ketika tidak ada interaksi dengan predator. Populasi predator diasumsikan mempunyai nilai ekonomi. Analisis Bionomik dan Kontrol pemanenan telah dikaji lebih lanjut. Hasil penelitian menunjukkan bahwa efek perlindungan prey mempengaruhi terhadap aktivitas pemanenan pada populasi sehingga mempengaruhi laba pada pemanenan predator. Beberapa simulasi perhitungan diberikan untuk mengkonfirmasi hasil analisis.
Kata Kunci: Pemanenan linear, Leslie-Gower Model, Bionomik, Perlindungan prey.

Published
2024-01-15
How to Cite
HUDA, Moh. Nurul et al. KONTROL OPTIMAL MODEL LESLIE-GOWER DENGAN PEMANENAN PADA POPULASI PREDATOR DAN PERLINDUNGAN PADA PREY. Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP), [S.l.], v. 15, n. 2, p. 73-82, jan. 2024. ISSN 2550-0422. Available at: <https://jos.unsoed.ac.id/index.php/jmp/article/view/8536>. Date accessed: 23 june 2024. doi: https://doi.org/10.20884/1.jmp.2023.15.2.8536.
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