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  4. On the bifurcation analysis of coral reef model subject to grazing intensity

On the bifurcation analysis of coral reef model subject to grazing intensity

MMC.
2025;
Volume 12, Number 1
: pp. 168–175
https://doi.org/10.23939/mmc2025.01.168
Received: December 16, 2024
Revised: February 16, 2025
Accepted: February 17, 2025

Zolkifli M. A. A., Safuan M. H., Roslan U. A. M.  On the bifurcation analysis of coral reef model subject to grazing intensity.  Mathematical Modeling and Computing. Vol. 12, No. 1, pp. 168–175 (2025)

Authors:
  1. M. A. A. Zolkifli
  2. M. H. Safuan
  3. U. A. M. Roslan
1
Akademi Intelek dan Data Analitik (AI.DA), Faculty of Applied Sciences and Technology, University Tun Hussein Onn Malaysia
2
Akademi Intelek dan Data Analitik (AI.DA), Faculty of Applied Sciences and Technology, University Tun Hussein Onn Malaysia
3
Special Interest Group for Modeling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, University Malaysia Terengganu

Coral reefs are complex ecosystems that serve as a habitat of diverse range of organism such as multispecies of fish, invertebrates, and marine plants.  Their role is also crucial in maintaining the health and balance of the surrounding environment.  However, as of present, the ecosystems are threatened by destructive and unresponsible fishing, climate change, and rising sea temperatures.  Hence, this study utilizes a mathematical model, building on insights from previous study, to investigate the impact of grazing intensity on coral – macroalgae interactions.  The objectives of this study are to extend the analysis of coral reef models analytically and numerically.  Linear stability analysis was performed to reveal the stability of each steady state and the corresponding bifurcation points were determined.  In result, we simulated bifurcation diagrams using MATCONT package to illustrate interactions between macroalgae and coral by varying macroalgae grazing intensity parameter.  The study found the presence of bistability behaviour in the system.  This result gave a deeper understanding of grazing intensity effects on coral reef ecosystems with different initial population.  The findings offer valuable insights for conservation and adaptive management strategies while facing environmental challenges.

coral reef
bifurcation
grazing intensity
linear stability analysis
bistability
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