Prey-predator dynamics with prey refuge providing additional food to predator

Highlights: • The effects of interplay between prey refugia and additional food are reported. • Hopf bifurcation conditions are derived analytically. • Existence of unique limit cycle is shown analytically. • Predator extinction may be possible at very high prey refuge ecological systems. - Abstract: The impacts of additional food for predator on the dynamics of a prey-predator model with prey refuge are investigated. The equilibrium points and their stability behaviours are determined. Hopf bifurcation conditions are derived analytically. Most significantly, existence conditions for unique stable limit cycle in the phase plane are shown analytically. The analytical results are in well agreement with the numerical simulation results. Effects of variation of refuge level as well as the variation of quality and quantity of additional food on the dynamics are reported with the help of bifurcation diagrams. It is found that high quality and high quantity of additional food supports oscillatory coexistence of species. It is observed that predator extinction possibility in high prey refuge ecological systems may be removed by supplying additional food to predator population. The reported theoretical results may be useful to conservation biologist for species conservation in real world ecological systems.