Stability, Sensitivity, and Bifurcation Analysis of a Rice–Pest Interaction Model

Tesa Nur Padilah; Iqbal Maulana

doi:10.37905/euler.v14i1.37529

Stability, Sensitivity, and Bifurcation Analysis of a Rice–Pest Interaction Model

Tesa Nur Padilah, Iqbal Maulana

Abstract

This study develops a five-dimensional mathematical model describing the interaction between rice and four major pests: rice stem borer, rat, brown planthopper, and rice bug. The existence and local stability of several equilibrium points are analyzed using linearization and the Routh–Hurwitz criterion. In addition, the global stability of the pest-free equilibrium point is established using Lyapunov’s direct method and LaSalle’s Invariance Principle. The results show that the pest-free equilibrium is globally asymptotically stable under certain threshold conditions related to the interaction and mortality parameters. Furthermore, a transcritical bifurcation is identified, which determines the transition between pest extinction and coexistence. Sensitivity analysis indicates that the rice bug parameters significantly influence the rice population, with proportional effects on the equilibrium state. Numerical simulations are performed to support the analytical results, including the dynamic behavior around the bifurcation threshold and the sensitivity of the rice population with respect to key parameters. The results highlight the importance of controlling pest interaction rates and increasing natural mortality to maintain the stability of the rice population.

Keywords

Rice–Pest Interaction; Nonlinear Dynamical System; Global Stability; Sensitivity Analysis; Transcritical Bifurcation

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DOI: https://doi.org/10.37905/euler.v14i1.37529