Stability analysis of Filippov prey–predator model with fear effect and prey refuge

Abstract

Mathematical ecosystems play a crucial role in our comprehension and conservation of ecology. Within these ecosystems, prey exhibits protective instincts that compel refuging behaviors to avoid predation risk. When the ratio of prey to predators falls below a threshold, prey seeks refuge. However, when prey is abundant relative to predators, these protective instincts are overridden as prey ventures out to forage. Therefore, this study develops a Filippov prey–predator model with fear effect on prey and switching of prey refuge behavior based on the ratio of prey to predators. Analytical and numerical approaches are used to address the dynamic behaviors, bifurcation sets, existence, and stability of various equilibria in this model. Additionally, the regions of sliding and crossing segments are analyzed. The bifurcation sets of pseudo-equilibrium and local and global sliding bifurcations are investigated. The numerical simulations are conducted to investigate the interplay between fear factor and other relevant parameters within the Filippov model, such as the threshold ratio and prey refuge. These investigations shed light on the influence of them in the model. The results indicate that increasing the fear factor results in a decrease in both prey and predator densities, thereby changing the behavior of the dynamics from a limit cycle oscillation to a stable state and vice versa. Notably, despite these population changes, neither species faces complete extinction.