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<p>This paper employs the Caputo fractional derivative to analyze a fractional-order prey–predator model distinguished by hyperbolic mortality, incorporating memory effects to augment the realism of species interactions. According to fixed point theory, it is proven that the system is well-posed ensuring the existence, uniqueness, positivity, and boundedness of the solution. Local stability is studied using the Jacobian matrix and fractional-order stability criteria. We conduct numerical simulations to corroborate the theoretical findings, and an error analysis utilizing step-size refinement demonstrates that the numerical scheme converges and is precise. Also, a sensitivity analysis is done to see how important parameters affect the dynamics of the system.</p>

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Study of memory-dependent dynamics of a predator–prey model with hyperbolic mortality

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • R. Mahalakshmi,
  • M. Sivakumar

摘要

This paper employs the Caputo fractional derivative to analyze a fractional-order prey–predator model distinguished by hyperbolic mortality, incorporating memory effects to augment the realism of species interactions. According to fixed point theory, it is proven that the system is well-posed ensuring the existence, uniqueness, positivity, and boundedness of the solution. Local stability is studied using the Jacobian matrix and fractional-order stability criteria. We conduct numerical simulations to corroborate the theoretical findings, and an error analysis utilizing step-size refinement demonstrates that the numerical scheme converges and is precise. Also, a sensitivity analysis is done to see how important parameters affect the dynamics of the system.