Turing patterns in exploited predator-prey systems with habitat loss

In this study, we explore the emergence of spatial patterns in a predator-prey model influenced by habitat loss, incorporating the effects of linear diffusion. By examining the stability of the system through the Jacobian matrix, we derive conditions for the occurrence of both Hopf and Turing bifurcations using analytical and numerical approaches. Numerical simulations yield Hopf bifurcation diagrams, revealing the system's dynamic responses to varying conditions. Our findings contribute to the understanding of how habitat loss and harvesting affect the spatial dynamics in predator-prey systems, which are described by partial differential equations (PDEs) under flux boundary conditions. We also investigate the impact of habitat loss due to harvesting on spatial patterns, identifying formations such as spots and stripes as a result of changes in harvesting efforts. We analytically derive the conditions for Turing instability, which are confirmed through numerical validation.