Pattern dynamics of a reaction-diffusion predator-prey system with both refuge and harvesting

We are concerned with a reaction-diffusion predator-prey model under homogeneous Neumann boundary condition incorporating prey refuge (proportion of both the species) and harvesting of prey species in this contribution. Criteria for asymptotic stability (local and global) and bifurcation of the subsequent temporal model system are thoroughly analyzed around the unique positive interior equilibrium point. For partial differential equation (PDE), the conditions of diffusion-driven instability and the Turing bifurcation region in two-parameter space are investigated. The results around the unique interior feasible equilibrium point specify that the effect of refuge and harvesting cooperation is an important part of the control of spatial pattern formation of the species. A series of computer simulations reveal that the typical dynamics of population density variation are the formation of isolated groups within the Turing space, that is, spots, stripe-spot mixtures, labyrinthine, holes, stripe-hole mixtures and stripes replication. Finally, we discuss spatiotemporal dynamics of the system for a number of different momentous parameters via numerical simulations.

Automated summary

The paper investigates a reaction-diffusion predator-prey model incorporating prey refuge and harvesting, analyzing asymptotic stability and bifurcation conditions to discuss the spatiotemporal dynamics of the system. The results suggest that the cooperation of refuge and harvesting plays a crucial role in controlling spatial pattern formation of the species. Computer simulations reveal typical dynamics of population density variation within the Turing space, including isolated groups like spots, stripe-spot mixtures, and labyrinthine patterns.