Turing instability and pattern induced by weak Allee effect and prey harvesting in a predator-prey model

Abstract We investigate the qualitative behavior of a predator-prey model with spatial diffusion, a weak Allee effect, and prey harvesting. In particular, we examine the boundedness of the solution of the diffusion-free model and the uniform persistence of the model, which ensure the long-term coexistence of species. In addition, the Turing instability condition induced by diffusion is derived through linear stability analysis. Finally, the theoretical results are illustrated by numerical simulations. The results of these numerical simulations demonstrate the effects of the harvesting and Allee effects on pattern formation. As the intensity of these factors changes, the model exhibits various spatial patterns, such as mixed spots and stripes, spots and circles, and pure spot patterns. Biologically, this indicates that the Allee effect and harvesting increase the risk of population extinction. These findings highlight the role of harvesting and the Allee effect in shaping spatial population structure.