Spatiotemporal Dynamics of a Predator-Prey System with Linear Harvesting Rate

We investigate a spatial ratio-dependent predator-prey system with linear harvesting rate. By using linear stability and bifurcation analysis, we obtain the conditions for Hopf and Turing bifurcation in the spatial domain. In addition, we classify spatial pattern formations of the system by making use of numerical simulations. In fact, the numerical simulations unveil that the typical Turing patterns, such as spotted, spot-stripelike mixtures and stripelike patterns, can be observed even if the system has the linear harvesting rate. In order to analyze these patterns via the spatial frequency, the discrete Fourier transform is used. Moreover, we discuss that the linear harvesting system is more realistic than a predator-prey system with constant harvesting. Our results disclose that the spatially extended system with linear harvesting rate has more complex dynamic patterns in the two-dimensional space. It may help to understand the effects of harvesting on species in the real world.