Impacts of refuge and additional foods on the spatiotemporal dynamics of a prey-predator system in a time-periodic environment

In this investigation, we study the dynamics of a diffusive prey-predator system in a time-periodic environment, incorporating prey refuge and supplementary food resources for predators. We establish solution’s boundedness, and derive the conditions for population persistence and extinction. We find that whenever both prey and predator populations persist, a unique periodic solution arises that is globally asymptotically stable. Our numerical results show that increasing prey refuge (or alternative food) stabilizes the system, shifting it from oscillatory behavior to stable coexistence. However, excessive alternative food availability can drive prey species to extinction, leaving predator as the sole surviving species. Further, we observe that a time-periodic environment significantly affects oscillatory patterns, driving transitions between uniform bulk oscillations and oscillating Turing patterns. Overall, our study highlights the crucial influence of time-periodic environmental factors on prey-predator dynamics, considering prey refuge and additional food for predators, and stresses the need to account for such variability in ecological systems.