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...

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Bibliographic Details
Published inActa applicandae mathematicae Vol. 176; no. 1
Main Authors Kumari, Nitu, Mohan, Nishith
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Bifurcation theory
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Diffusion
Dirichlet problem
Food chains
Mathematics
Mathematics and Statistics
Ordinary differential equations
Partial Differential Equations
Population density
Predator-prey simulation
Predators
Probability Theory and Stochastic Processes
Maximum principles
35B45
35B32
Semitrivial solutions
Bifurcation theory
Nonlinear eigenvalue problem
35B09
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Summary: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.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-021-00455-w