Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction
Wonlyul Ko Inkyung Ahn
Communications on Pure & Applied Analysis 2018, 17(2): 375-389 doi: 10.3934/cpaa.2018021

We consider a predator-prey system with a ratio-dependent functional response when a prey population is infected. First, we examine the global attractor and persistence properties of the time-dependent system. The existence of nonconstant positive steady-states are studied under Neumann boundary conditions in terms of the diffusion effect; namely, pattern formations, arising from diffusion-driven instability, are investigated. A comparison principle for the parabolic problem and the Leray-Schauder index theory are employed for analysis.

keywords: Non-constant positive steady states eco-epidemiological model predator-prey interaction global attractor pattern formation
Asymptotic behavior of a ratio-dependent predator-prey system with disease in the prey
Inkyung Ahn Wonlyul Ko Kimun Ryu
Conference Publications 2013, 2013(special): 11-19 doi: 10.3934/proc.2013.2013.11
In this paper, we consider a ratio-dependent predator-prey model with disease in the prey under Neumann boundary condition. we construct a global attractor region for all time-dependent non-negative solutions of the system and investigate the asymptotic behavior of positive constant solution. Furthermore, we also study the asymptotic behavior of the non-negative equilibria.
keywords: predator-prey disease-free asymptotic stability. Ratio-dependent

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