Complex Dynamics of a Ratio-Dependent Predator-Prey Model Induced by Spatial Motion

One of the most efficient predator-prey models with spatial effects is the one with ratio-dependent functional response. However, there is a need to further explore the effects of spatial motion on the dynamic behavior of population. In this work, we study a ratio-dependent predator-prey model with diffusion terms. The aim of this work is to investigate the changes in predator's distribution in space as the prey populations change their mobility. We observe that the frequency diffusion of the prey gives rise to the sparse density of the predator. Moreover, we also observe that the increasing rate of the conversion into predator biomass induces pattern transitions of the predator. Specifically speaking, Turing pattern of the predator populations goes gradually from a spotted pattern to a black-eye pattern, with the intermediate state being the mixture of spot and stripe pattern. The simulation results and analysis of this work illustrate that the diffusion rate and the real intrinsic factor influence the persistence of the predator-prey system mutually.

Automated summary

The study shows that the frequency diffusion of prey leads to a sparse density of predators. Increasing the conversion rate into predator biomass may induce pattern transitions of the predator, from a spotted pattern to a black-eye pattern, with an intermediate state of a mixture of spot and stripe patterns. The simulation results and analysis demonstrate that the diffusion rate and the intrinsic factor mutually influence the persistence of the predator-prey system.