Nisa', Anastasya Choirun
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Stability Analysis of a Three-Trophic Rice Ecosystem with Holling II and Crowley–Martin Responses Nisa', Anastasya Choirun; Savitri, Dian
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40204

Abstract

This study examines three-trophic-level ecological dynamics in rice field ecosystems involving rice as the producer, brown planthoppers (Nilaparvata lugens) as herbivores, and Pardosa sp. spiders as top predators. Population interactions were modeled using logistic growth for rice and two response functions: the Holling type II response for planthopper predation on rice, and the Crowley–Martin response for Pardosa sp. predation on planthoppers to capture predatorinterference. The resulting model was formulated as a system of nonlinear differential equations.Analytically, four equilibrium points were obtained: total population extinction, extinction of planthoppers and Pardosa sp., extinction of Pardosa sp., and coexistence of all threespecies. Local stability analysis at each equilibrium point was conducted using the Jacobian matrix and the Routh–Hurwitz criterion. Numerical simulations were performed for severalparameter combinations by varying planthopper growth efficiency and Pardosa sp. predation intensity. The simulation results were consistent with the theoretical analysis and showed that small changes in biological parameters could shift the system from stable coexistence to near extinction of the planthopper population. Ecologically, the model demonstrates that rice field ecosystem balance is strongly influenced by the interaction between planthopperreproductive capacity and the predatory strength of Pardosa sp., providing a theoretical basisfor sustainable planthopper pest control strategies.