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<p>Prey–predator interactions are modeled using various dynamical systems and these interactions are affected by several factors. The predation rate of prey, reproduction rate, and prey use various strategies to avoid predation, the movement of the prey and predator species, food, and secured shelter can lead to the emergence of various types of patterns. These patterns in the prey–predator dynamics explain the complicated ecosystem. A reaction-diffusion prey–predator model with harvesting in predator is numerically investigated. A conditionally positivity preserving scheme is used. The von Neumann technique is used for the stability analysis. The Taylor series is used for the consistency analysis and discrete approximation is consistent with the underlying model. Pattern formation is observed for the governing model. The spot, stripe, and spot-stripes patterns are successfully gained that describe the complicated dynamics of the prey–predator dynamics. 3D and 2D simulations are drawn for the underlying model. The underlying model has two equilibria, both are successfully gained. All the theoretical results are verified through the simulations.</p>

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Mathematical analysis and pattern formation in diffusive predator–prey system

  • 期刊论文

  • 发表日期：

    2025年1月7日

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  • Nauman Ahmed,
  • Muhammad Waqas Yasin,
  • Ali Akgül,
  • Dumitru Baleanu,
  • Ovidiu Tintareanu-Mircea

摘要

Prey–predator interactions are modeled using various dynamical systems and these interactions are affected by several factors. The predation rate of prey, reproduction rate, and prey use various strategies to avoid predation, the movement of the prey and predator species, food, and secured shelter can lead to the emergence of various types of patterns. These patterns in the prey–predator dynamics explain the complicated ecosystem. A reaction-diffusion prey–predator model with harvesting in predator is numerically investigated. A conditionally positivity preserving scheme is used. The von Neumann technique is used for the stability analysis. The Taylor series is used for the consistency analysis and discrete approximation is consistent with the underlying model. Pattern formation is observed for the governing model. The spot, stripe, and spot-stripes patterns are successfully gained that describe the complicated dynamics of the prey–predator dynamics. 3D and 2D simulations are drawn for the underlying model. The underlying model has two equilibria, both are successfully gained. All the theoretical results are verified through the simulations.