Luthfi, Muhammad and Prof. Dr. Agus Suryanto, M.Sc., and Prof. Dr. Isnani Darti, S.Si., M.Si. (2024) Model Interaksi Hama - Musuh Alami - Tanaman Refugia dengan Kompetisi Intra-spesies pada Musuh Alami. Magister thesis, Universitas Brawijaya.
Abstract
Pada tesis ini, dikonstruksi model interaksi hama - musuh alami - tanaman refugia dengan kompetisi intra-spesies pada musuh alami. Pada model tersebut diasumsikan terdapat tiga populasi, yaitu populasi hama (X), populasi musuh alami (Y ), dan populasi tanaman refugia (Z). Telah dibuktikan eksistensi, ketunggalan, kepositifan, dan keterbatasan solusi. Dari hasil analisis, diperoleh tujuh titik kesetimbangan, yaitu titik kepunahan ketiga populasi (E0), titik kepunahan hama dan musuh alami (E1), titik kepunahan musuh alami dan tanaman refugia (E2), titik kepunahan musuh alami (E3), titik kepunahan hama (E4), titik kepunahan tanaman refugia (E5), dan titik koeksistensi (E6). Berdasarkan hasil analisis kestabilan, titik kesetimbangan E0, E1, E2, dan E5 bersifat tidak stabil, sedangkan titik kesetimbangan E3, E4, dan E6 bersifat stabil asimtotik lokal dan global dengan syarat tertentu. Model mengalami bifurkasi Hopf di sekitar titik koeksistensi E6. Hasil simulasi numerik mengonfirmasi hasil analisis yang telah diperoleh.
English Abstract
In this study, we introduce a model that describes the interaction among pests, predators, and refugia plants, incorporating intraspecific competition within the predator population. The existence, uniqueness, non-negativity, and boundedness of the solutions are shown to ensure that the proposed model is biologically feasible. We perform dynamical analysis to identify all potential equilibrium points and examine their both local and global stability characteristics. The model has seven equilibrium points, namely the trivial equilibrium point (E0), the refugia plant-only equilibrium point (E1), the pest-only equilibrium point (E2), the pest-refugia plant equilibrium point (E3), the pest-free equilibrium point (E4), the pest-predator equilibrium point (E5), and the coexistence equilibrium point (E6). However, only E3, E4, and E6 are locally and globally stable under certain conditions. Furthermore, we show that the system exhibits a Hopf bifurcation around the E6. Finally, we confirm our analytical results through some numerical simulations.
| Item Type: | Thesis (Magister) |
|---|---|
| Identification Number: | 0424090083 |
| Uncontrolled Keywords: | hama, musuh alami, tanaman refugia, kestabilan lokal dan global, bifurkasi Hopf, simulasi numerik. |
| Divisions: | S2/S3 > Magister Biologi, Fakultas MIPA |
| Depositing User: | Unnamed user with username nova |
| Date Deposited: | 04 Feb 2025 04:51 |
| Last Modified: | 04 Feb 2025 04:51 |
| URI: | http://repository.ub.ac.id/id/eprint/235565 |
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