ANALISIS MODEL PREDATOR-PREY ECENG GONDOK DENGAN IKAN GRASS CARP DAN PEMANENAN

Dwi Fahmi Ilmiawan, Muhammad Kharis, Supriyono Supriyono

Abstract


Eceng gondok merupakan tanaman invasif yang perlu dikontrol. Pengontrolan dapat dilakukan dengan menggunakan ikan Grass carp dan pemanenan. Interaksi pada pengontrolan tersebut dinamakan model predator-prey dengan pemanenan. Artikel ini membahas tentang sistem dinamik model predator-prey pada populasi eceng gondok dengan adanya ikan Grass carp dan pemanenan. Model ini menggunakan fungsi respon Holling tipe III, karena sesuai dengan ikan Grass carp yang cenderung mencari mangsa lain ketika eceng gondok mulai berkurang. Secara analitik, terdapat tiga titik ekuilibrium yakni 𝐸0, 𝐸1, dan 𝐸2 dengan beberapa syarat batas. Kestabilan dari ketiga titik ekuilibrium dalam sembilan kasus yang berbeda merupakan stable node point, stable spiral point, center point, unstable saddle point, unstable node point, dan unstable spiral point. Hasil simulasi numerik menunjukkan sifat yang sama untuk sembilan kasus kestabilan tersebut. Jadi, solusi yang dapat dilakukan untuk mengontrol populasi eceng gondok yakni dengan memusnahkan kedua populasi, memusnahkan populasi ikan Grass carp, dan melestarikan kedua populasi.

 

Water hyacinth is an invasive plant that needs to be controlled. Control can be performed using Grass carp fish and harvesting. Interaction in the control process called predator-prey model with harvesting. This article discussed about the system dynamic of predator-prey model on water hyacinth population with Grass carp fish and harvesting. This model uses Holling response function of type III, because according to the Grass carp fish that tend to seek other prey when water hyacinth began to decrease. Analytically, there are three equilibrium points namely 𝐸0, 𝐸1, and 𝐸2 with some boundary conditions. The stability of the three equilibrium points in nine different cases are stable node point, stable spiral point, center point, unstable saddle point, unstable node point, and unstable spiral point. Numerical simulation results showed the same properties for the stability of the nine cases. So, the solution that can be done to control the water hyacinth population are the eradicate both populations, eradicate of Grass carp fish population, and conserve both populations.


Keywords


Water hyacinth; Grass carp fish; predator-prey model; harvesting; the equilibrium point

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References


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