Combining impact of velocity, fear and refuge for the predator-prey dynamics

We develop a deterministic predator-prey compartmental model to investigate the impact of their velocities on their interactions. Prey hides in a refuge area and comes out of this area when predation pressure declines. To avoid predation, prey can limit their velocity. For antipredator behaviour, we examined that prey mortality increases when either predator or prey velocity increases while raising antipredator behaviour increases prey density. We proved that predator free equilibrium is globally asymptotically stable and co-existing equilibrium will be globally stable under certain conditions. We find that transcritical bifurcations occur at predator-free equilibrium at the certain value of the death rate of the predator.

Automated summary

We developed a deterministic predator-prey compartmental model to study the impact of their velocities on interactions. The prey hides in a refuge area and emerges when predation pressure declines, with the ability to limit their velocity to avoid predation. We found that increased predator or prey velocity leads to higher prey mortality, while raising antipredator behavior increases prey density. We also proved the global asymptotic stability of the predator-free equilibrium and the global stability of the co-existing equilibrium under certain conditions. Transcritical bifurcations were observed at a specific value of the predator's death rate.