Spatio-temporal dynamics of a predator–prey system with variable carrying capacity and Cosner response function

The environmental carrying capacity plays a major role in population dynamics and is highly unpredictable in predator–prey relationships. In this study, we examine a predator–prey model with logistic growth rate and variable carrying capacity of prey species. The predator–prey interaction is governed by the Cosner functional response. Analysis of the feasibility of equilibria and their stability conditions are done. To reflect the reality that prey and predator populations actively move within biologically relevant spatial regions, we also investigate the corresponding spatio-temporal model. The diffusive model is analyzed for the existence of Turing instability. Further, some noteworthy numerical techniques are applied to investigate the dynamics of predator–prey system in the absence as well as presence of diffusion. Our numerical results suggest that increasing the predator handling time may stabilize the system by suppressing the persistent oscillations. However, the carrying capacity of the prey population alter system stability, facilitating the transition to a stable limit cycle from stable scenario. Moreover, we discover that the prey and predator populations in the ecosystem exhibit distinct spatial patterns over time.