Additional Food Induced Turing Patterns for a Diffusive Predator–Prey Model

Abstract

We present a diffusive ratio-dependent predator–prey model with additional food supply to predators and investigate the spatiotemporal dynamics induced as a result of this additional food supply. We firstly, consider the co-existential equilibrium for the temporal model and discuss its local stability properties. We then carry out the local stability analysis of this co-existential equilibrium point for the spatiotemporal model. Secondly, we derive the parametric conditions under which Turing instability (i.e., the co-existential equilibrium point is stable for the temporal model but is unstable with respect to the spatiotemporal model) can occur as a result of additional food being added to the system. We also show that Turing bifurcation takes place and a spatially heterogeneous pattern emerges over time. Finally, the corresponding Turing patterns are revealed by way of simulations. In conclusion, we observe the important role of the quality and quantity of additional food in order for the Turing instability to occur even for parameter values for which the co-existential equilibrium of the original ratio-dependent model either does not exist or is unstable.