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<p>In this research, we study a fractional-order (FDE) three-species food chain model with predator harvesting and prey refuge. In the analytical results of the fractional calculus, the existence, uniqueness, non-negativity, and uniform boundedness of solutions are rigorously established. Boundedness of solutions in fractional calculus. Lyapunov-based stability analysis is used to determine necessary requirements for local and global asymptotic stability of all biologically important equilibrium points. Numerical simulations in MATLAB confirm the analytical results and show that moderate prey refuge supports asymptotic stability while the introduction of predator harvesting destabilizes the ecological equilibrium dramatically. A critical chaotic-to-stable transition controlled by the fractional order parameter q when varying q from 0 to 1 reveals the significant impact of memory effects in determining the long-term population dynamics. The fractional-order model is more sensitive to ecological interventions than the standard integer-order model and has more flexibility in describing complicated ecological processes. These results underline the importance of adaptive parameter control for ecosystem sustainability and prove fractional order modeling to be a potent and biologically relevant tool for ecological study and conservation planning.</p>

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Dynamics of a fractional-order three-species food chain model with predator harvesting and prey refuge

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月21日

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  • Geremew Kenassa Edessa,
  • S. Hariprasad,
  • N. Phani Kumar,
  • D. Manohar,
  • M. A. S. Srinivas,
  • K. V. L. N. Acharyulu

摘要

In this research, we study a fractional-order (FDE) three-species food chain model with predator harvesting and prey refuge. In the analytical results of the fractional calculus, the existence, uniqueness, non-negativity, and uniform boundedness of solutions are rigorously established. Boundedness of solutions in fractional calculus. Lyapunov-based stability analysis is used to determine necessary requirements for local and global asymptotic stability of all biologically important equilibrium points. Numerical simulations in MATLAB confirm the analytical results and show that moderate prey refuge supports asymptotic stability while the introduction of predator harvesting destabilizes the ecological equilibrium dramatically. A critical chaotic-to-stable transition controlled by the fractional order parameter q when varying q from 0 to 1 reveals the significant impact of memory effects in determining the long-term population dynamics. The fractional-order model is more sensitive to ecological interventions than the standard integer-order model and has more flexibility in describing complicated ecological processes. These results underline the importance of adaptive parameter control for ecosystem sustainability and prove fractional order modeling to be a potent and biologically relevant tool for ecological study and conservation planning.