Model matematis predator-prey tanaman padi, hama penggerek batang, tikus, dan wereng batang coklat di Karawang - Tesa Nur Padilah; Betha Nurina Sari; Hannie Hannie (Department of Mathematics Education, Faculty of Mathematics and Natural Sciences, UNY, 2018)
Karawang merupakan salah satu pusat penanaman padi di Pulau Jawa. Keberhasilan panen dapat terganggu oleh adanya organisme pengganggu tumbuhan (OPT) sehingga dapat mengancam target swasembada beras. Hubungan antara tanaman padi dengan OPT dapat dibentuk menjadi suatu model matematis yaitu model predator-prey. Untuk itu, penelitian ini bertujuan untuk menganalisis model matematis predator-prey tanaman padi dan OPT. Predator (pemangsa) adalah makhluk hidup yang memakan mangsa (prey). Model predator-prey antara tanaman padi dengan OPT yang dibahas adalah model tiga predator yaitu hama penggerek batang, tikus, dan wereng batang coklat dengan prey yaitu padi. Pertumbuhan padi mengikuti model pertumbuhan logistik. Model yang diturunkan berbentuk sistem persamaan diferensial nonlinier. Pada model diperoleh lima titik ekuilibrium. Analisis perilaku model dilakukan pada tiga titik ekuilibrium dan ketiganya bersifat stabil asimtotik. Simulasi model dengan menggunakan software Maple 13 sejalan dengan analisis perilaku model. Faktor-faktor yang berpengaruh agar populasi hama penggerek batang, tikus, dan wereng batang coklat dapat menurun bahkan hilang dari populasi yaitu tingkat kematian alami serta tingkat interaksi padi terhadap hama-hama tersebut. Predator-prey mathematical model of rice plants, stem borer, rat, and brown planthopper in Karawang AbstractKarawang was one of the center of rice planting in Java Island. The success of the harvest may be disrupted by the presence of plant pest organisms that may threaten the rice self-sufficiency target. The relationship between rice plants and pests can be formed into a mathematical model, that was a predator-prey model. Therefore, this research aimed to analyze the mathematical model of predator-prey between rice plants and plant pest organisme. Predators were living things that eat prey. The predator-prey model between rice plants and pests discussed was a three predator model of stem borer, rat, and brown stem rhizome with the prey, that was rice. Rice growth follows the logistic growth model. The derived model was an nonlinear differential equation system. In this model obtained five equilibrium points. Model behavioral analysis was performed on three equilibrium points and they were stable asymptotically. Simulations of the model using Maple 13 software were in good agreement with behavioral analysis model. Factors that influence the stem borer, rat, and brown planthopper population could decrease even disapear from the population were the natural death rate and the interaction rate of rice to the pests.