Positive Coexistence of Steady States for a Diffusive Ratio-Dependent Predator-Prey Model with an Infected Prey. (6th May 2015)

• Record Type: Journal Article
• Authors: Kim, Kwangjoong; Ahn, Inkyung
• Other Names: Hudzik Henryk Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-05-06
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/810451
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We examine a diffusive ratio-dependent predator-prey system with disease in the prey under homogeneous Dirichlet boundary conditions with a hostile environment at its boundary. We investigate the positive coexistence of three interacting species (susceptible prey, infected prey, and predator) and provide nonexistence conditions of positive solutions to the system. In addition, the global stability of the trivial and semitrivial solutions to the system is studied. Furthermore, the biological interpretation based on the result is also presented. The methods are employed from a comparison argument for the elliptic problem as well as the fixed-point theory as applied to a positive cone on a Banach space.