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<p>This study uses the Holling type-II functional response (HT-II FR) to analyze the dynamics of a three-species, prey-dependent Food Chain Model (FCM) in order to identify the impact of nonlinear prey harvesting on the system. The system’s behaviour near its biologically possible equilibrium is thoroughly examined. The dynamical system is shown to be positive, bounded, and dissipative. To investigate the system’s behaviour, a stability study of the equilibria, including their global as well as local stability, is performed. Additionally, a Global Stability (GS) study was performed using the proper Lyapunov functions. The proposed model exhibits two types of bifurcations under certain conditions: Hopf bifurcation (HPB) and Saddle-Node bifurcation (SNB). An analysis of SNB is conducted with the harvesting rate as the bifurcation parameter. At the equilibrium point where all three species coexist, the system undergoes an SNB, which has significant implications for ecological stability. When appropriate parameter values are chosen, the model also exhibits HPB. To validate the analytical findings, numerical simulations are performed to demonstrate and support the theoretical results.</p>

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Analyzing the Global Behaviour Using the Lyapunov–Lasalle Invariance Principle of a Three Species Food Chain Model with Nonlinear Prey Harvesting and Predator–Prey Refuge

  • 期刊论文

  • 发表日期：

    2025年8月26日

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  • Imran Ali,
  • Jayanta Mahato,
  • Paritosh Bhattacharya

摘要

This study uses the Holling type-II functional response (HT-II FR) to analyze the dynamics of a three-species, prey-dependent Food Chain Model (FCM) in order to identify the impact of nonlinear prey harvesting on the system. The system’s behaviour near its biologically possible equilibrium is thoroughly examined. The dynamical system is shown to be positive, bounded, and dissipative. To investigate the system’s behaviour, a stability study of the equilibria, including their global as well as local stability, is performed. Additionally, a Global Stability (GS) study was performed using the proper Lyapunov functions. The proposed model exhibits two types of bifurcations under certain conditions: Hopf bifurcation (HPB) and Saddle-Node bifurcation (SNB). An analysis of SNB is conducted with the harvesting rate as the bifurcation parameter. At the equilibrium point where all three species coexist, the system undergoes an SNB, which has significant implications for ecological stability. When appropriate parameter values are chosen, the model also exhibits HPB. To validate the analytical findings, numerical simulations are performed to demonstrate and support the theoretical results.