<p>Mathematical ecosystem plays a crucial role in the conservation of ecosystem of the Sundarbans. In this ecosystem, prey exhibits protective instincts that compel refuging behaviors to avoid predation risk. Prey seeks refuge, when the ratio of prey to predator’s threshold falls below. However, when prey is plentiful relative to predators, these defensive instincts are suspended as prey ventures out to grazing. Therefore, this study introduces a Filippov prey-predator model incorporating both fear-driven migration and density-dependent prey refuge mechanisms. Numerical computation approaches are used to address the ecological behaviors, bifurcation sets, existence, and stability of various equilibria in this model. Moreover, we analyzed the regions of sliding and crossing segments. We also investigated the bifurcation sets of pseudo-equilibrium and local and global sliding bifurcations. The numerical simulations are managed to investigate the adaptability between fear factor and other relevant parameters within the Filippov model, such as the threshold ratio and prey refuge. These investigations focus on the influence of them in the model. These results indicate that increasing the fear factor in prey decreases predator densities; thereby it changes the ecological behaviors from a limit cycle oscillation to a stable state and vice versa. Notably, regardless of these population changes, neither species faces complete extinction.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Fear-Driven Dynamics and Refuge Thresholds in a Filippov Prey-Predator Model: Insights into the Sundarbans’ Ecosystem

  • Nazmul Hasan,
  • Haider Ali Biswas,
  • Nomah Maan,
  • Sharif Uddin

摘要

Mathematical ecosystem plays a crucial role in the conservation of ecosystem of the Sundarbans. In this ecosystem, prey exhibits protective instincts that compel refuging behaviors to avoid predation risk. Prey seeks refuge, when the ratio of prey to predator’s threshold falls below. However, when prey is plentiful relative to predators, these defensive instincts are suspended as prey ventures out to grazing. Therefore, this study introduces a Filippov prey-predator model incorporating both fear-driven migration and density-dependent prey refuge mechanisms. Numerical computation approaches are used to address the ecological behaviors, bifurcation sets, existence, and stability of various equilibria in this model. Moreover, we analyzed the regions of sliding and crossing segments. We also investigated the bifurcation sets of pseudo-equilibrium and local and global sliding bifurcations. The numerical simulations are managed to investigate the adaptability between fear factor and other relevant parameters within the Filippov model, such as the threshold ratio and prey refuge. These investigations focus on the influence of them in the model. These results indicate that increasing the fear factor in prey decreases predator densities; thereby it changes the ecological behaviors from a limit cycle oscillation to a stable state and vice versa. Notably, regardless of these population changes, neither species faces complete extinction.