Dynamical System Analysis of the Prey-predator Interactions involving Prey Refuge and Herd Behaviors in Preys

Abstract

By employing a prey refuge mechanism, more preys can be protected from predation. Prey species are also better protected from predation when they congregate in herds. However, what if the prey refuge and herd behavior mechanisms were combined in a system? To investigate this phenomenon, we consider two different prey-predator systems with prey refuge capacity. The first system is a simple prey-predator with prey refuge, whereas the second system considers prey refuge and prey herd behavior mechanisms. Using these models, we explore how different prey refuge strategies affect species interactions in both systems. To accomplish this, we use theoretical techniques (e.g., computing steady states and performing the stability analysis) and numerical bifurcation analysis to demonstrate various dynamical behaviors of these two prey-predator systems. Once prey refuge is treated as a bifurcation parameter, we observe the occurrence of supercritical Hopf and transcritical bifurcations in both systems. Furthermore, we explore the dynamic effects of prey refuge and predator handling time on species population interactions: our findings reveal that using both prey refuge and herd behavior as escape strategies; it is possible to dilute the predation pressure and ensure species biodiversity.

The Effects of Varying Predator Dispersal Strength on Prey-Predator Dynamics with Refuge Process

“…The range of m < 0.7 is excluded from our analysis due to the presence of unstable dynamics regions. Interested readers are referred to previous work [13] on these unstable dynamics for further detail.…”

“…By substituting each of the steady states (i) -(iii) into the Jacobian matrix, we can calculate the corresponding eigenvalues. The stability analysis of these three steady states is thoroughly discussed in the work of [13]. The eigenvalues provide insights into the stability properties of the steady states, shedding light on whether small perturbations will dampen out or amplify over time.…”

“…Das and Samanta [12] investigated a model with refuge and additional food for predators in a fluctuating environment, revealing the complex interactions between refuge availability, predator foraging behaviour, and environmental fluctuations. Manaf and Mohd [13] considered not only prey refuge but also herd behaviours in prey species, uncovering the stability and bifurcational change in dynamics of these systems.…”