Model Modifikasi Holling-Tanner dengan Interaksi Kanibalisme dan Sumber Makanan Alternatif pada Predator

Rian Ade Pratama, Dessy R Suryani, Maria F V Ruslau

Abstract


Penelitian ini mengkaji model pertumbuhan populasi model predator-prey Holling-Tonner yang dimodifikasi. Pertumbuhan model predator-prey yang dianalisis mengadopsi pertumbuhan logistik. Sementara pada fungsi pemangsaan mengikuti model Holling Type II. Variabel yang tidak kalah penting dalam penelitian ini adalah adanya sumber alternatif bagi predator. Konsep seperti ini sangat realistis untuk dipertimbangkan, mengingat banyak spesies predator yang berganti sumber makanan, dikarenakan sumber makanan yang terbatas. Analisis kestabilan dilakukan pada model untuk melihat keberlangsungan populasi dalam jangka waktu yang lama dengan tingkat interaksi yang sesuai. Dari empat titik equilibrium non-negatif yang dihasilkan pada model, pengujian kestabilan hanya dilakukan pada satu titik equilibrium. Secara matematis dilakukan uji Routh-Hurwitz, dengan matriks Jacobian yang bersesuaian. Simulasi numerik menjadi asumsi realistis awal bagi keberlangsungan hidup masing-masing spesies dan melihat karakter dari masing-masing spesies tersebut. Titik equilibrium yang dipilih menjadi pegujian pada kesetabilan asimtotik lokal dan kurva pertumbuhan. Kemungkinan adanya perpindahan sumber makanan sangat mungkin terjadi, sementara interaksi kanibalisme pada model yang dikembangkan tidak memberikan pengaruh yang signifikan pada masing-masing spesies.

 

Kata Kunci:  Kanibalisme, makanan alternatif dan Predator-Prey.


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DOI: http://dx.doi.org/10.24014/jsms.v8i2.17356

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