Coexistence States of a Ratio-Dependent Predator-Prey Model with Nonlinear Diffusion

In this work, we consider a two species ratio-dependent food chain model with nonlinear diffusion terms. Using bifurcation theory and a priori estimates we prove the existence of positive solution set for the model system. Through our bifurcation theory based analysis, we were able to conclude that a ratio-dependent predator-prey model with nonlinear or cross diffusion can coexist in a habitat surrounded by an inhospitable environment represented by the Dirichlet boundary conditions. Also we were able to show that bifurcation theory can be successfully employed to comment on the existence of positive solutions of a model system where interaction is in accordance with a predator dependent functional response.

Automated summary

This study investigates a two species ratio-dependent food chain model with nonlinear diffusion terms using bifurcation theory and a priori estimates to prove the existence of positive solution set for the model system. The analysis concludes that a ratio-dependent predator-prey model with nonlinear or cross diffusion can coexist in a habitat surrounded by an inhospitable environment represented by the Dirichlet boundary conditions. Additionally, the successful employment of bifurcation theory in commenting on the existence of positive solutions of a model system where interaction is in accordance with a predator dependent functional response is demonstrated.