Analysis of Mangrove Forest Resource Depletion Models due to The Opening of Fish Pond Land with Time Delay

Ummi Usrotus Saydatul Wakhidah; Kartika Nugraheni; Winarni Winarni

doi:10.19184/jid.v23i1.23889

Ummi Usrotus Saydatul Wakhidah Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan
Kartika Nugraheni Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan
Winarni Winarni Program Studi Matematika, Jurusan Matematika dan Teknologi Informasi, Institut Teknologi Kalimantan

DOI: https://doi.org/10.19184/jid.v23i1.23889

Abstract

Mangrove forest is an ecosystem with many resources and high biological diversity that contain many species of animal, such as proboscis monkeys. One of the problems that keep happening on mangrove forest is the opening of fish pond. Opening of fish pond can damage mangrove resource by the degradation of the mangrove habitat. This study aims to analyze the depletion stability model of mangrove forest resources with time delay, and to show effect of time delay and the presence of change in the equilibrium point (Hopf bifurcation) on depletion stability model of mangrove forest resources due to fish pond openings. The depletion stability model of mangrove forest resources can be modeled as a system of nonlinear differential equations. In the numerical simulation results, critical value of delay (τ₀) is 7.05 and the transverse conditions are not fulfilled. This mean there is no change in stability and the delay time parameter (τ) does not affect the stability of the system. System will remain stable when the mangrove forests, proboscis monkeys, and fish ponds are in equilibrium. In other words, mangrove forests, proboscis monkeys, and fish ponds can coexist even though time delays, and the analysis using the Hopf bifurcation cannot be carried out.

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