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<p>This study develops a holistic mathematical model unifying three key mechanisms: fear-induced prey behavioral changes, cooperative predator hunting, and linear harvesting. The prey population follows logistic growth, modulated by a fear function that reduces reproduction based on predator density. Predation is modeled using a modified Holling Type II functional response, capturing cooperative hunting efficiency and saturation effects. Harvesting terms reflect realistic exploitation scenarios for both species. Using bifurcation theory, we identify saddle-node, transcritical, Bogdanov–Takens, and Hopf bifurcations, and analyze stability via Lyapunov exponents. Results reveal that fear effects stabilize dynamics by suppressing prey growth, while cooperative hunting enhances predation efficiency, potentially destabilizing coexistence. Linear harvesting introduces critical thresholds beyond which extinction occurs. Sensitivity analysis identifies sustainable harvesting strategies, balancing ecological persistence and resource extraction. Numerical simulations are carried out to validate the theoretical findings.</p>

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Analysis of Predator–Prey Systems Incorporating Prey Fear, Cooperative Predation, and Harvesting

  • 期刊论文

  • 发表日期：

    2026年4月2日

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  • Md. Sabiar Rahman,
  • Biswajit Saha

摘要

This study develops a holistic mathematical model unifying three key mechanisms: fear-induced prey behavioral changes, cooperative predator hunting, and linear harvesting. The prey population follows logistic growth, modulated by a fear function that reduces reproduction based on predator density. Predation is modeled using a modified Holling Type II functional response, capturing cooperative hunting efficiency and saturation effects. Harvesting terms reflect realistic exploitation scenarios for both species. Using bifurcation theory, we identify saddle-node, transcritical, Bogdanov–Takens, and Hopf bifurcations, and analyze stability via Lyapunov exponents. Results reveal that fear effects stabilize dynamics by suppressing prey growth, while cooperative hunting enhances predation efficiency, potentially destabilizing coexistence. Linear harvesting introduces critical thresholds beyond which extinction occurs. Sensitivity analysis identifies sustainable harvesting strategies, balancing ecological persistence and resource extraction. Numerical simulations are carried out to validate the theoretical findings.