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<p>In this paper, we explore the Leslie–Gower type prey–predator model with a Holling-IV functional response, examining both deterministic and stochastic environments. In the deterministic analysis, we establish the positivity and boundedness of solutions, as well as the stability criteria for various equilibria and different bifurcations, including transcritical, saddle-node, and Hopf bifurcations. For the stochastic component, we demonstrate the existence and uniqueness of global positive solutions and identify conditions for persistence in the mean. Additionally, we derive the stationary distribution and probability density function for the stochastic model. We conduct a stochastic sensitivity analysis by approximating the confidence domain, showing that the size of the confidence ellipse is influenced by the level of noise intensity. When the confidence ellipse intersects the separatrix, critical transitions or tipping points may occur. In such instances, the system may not revert to its previous state depending on the intensity of fluctuations. Most theoretical findings are supported by numerical simulations.</p>

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Dynamic complexities of a modified Leslie–Gower model in deterministic and stochastic environments

  • 期刊论文

  • 发表日期：

    2025年1月20日

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  • Pritam Saha,
  • Akidul Haque,
  • Md. Shahidul Islam,
  • Uttam Ghosh

摘要

In this paper, we explore the Leslie–Gower type prey–predator model with a Holling-IV functional response, examining both deterministic and stochastic environments. In the deterministic analysis, we establish the positivity and boundedness of solutions, as well as the stability criteria for various equilibria and different bifurcations, including transcritical, saddle-node, and Hopf bifurcations. For the stochastic component, we demonstrate the existence and uniqueness of global positive solutions and identify conditions for persistence in the mean. Additionally, we derive the stationary distribution and probability density function for the stochastic model. We conduct a stochastic sensitivity analysis by approximating the confidence domain, showing that the size of the confidence ellipse is influenced by the level of noise intensity. When the confidence ellipse intersects the separatrix, critical transitions or tipping points may occur. In such instances, the system may not revert to its previous state depending on the intensity of fluctuations. Most theoretical findings are supported by numerical simulations.