Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction
Wonlyul Ko Inkyung Ahn

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
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
Asymptotical behaviors of a general diffusive consumer-resource model with maturation delay
Wonlyul Ko Inkyung Ahn Shengqiang Liu
In this paper, we examine the asymptotic behaviors of a diffusive delayed consumer-resource model subject to homogeneous Neumann boundary conditions, where the discrete time delay covers the period from the birth of juvenile consumers to their maturity, and the predation is of a general type of functional response. We construct the threshold dynamics of the persistence and extinction of the consumer. Moreover, we establish the sufficient conditions for the global attractivity of the semitrivial and coexistence equilibria. Finally, we apply our results to the specific consumer-resource models with Beddington-DeAngelis, Crowley-Martin, and ratio-dependent type of functional responses.
keywords: permanence global stability Beddington-DeAngelis/Crowley-Martin/ratio-dependent models. Lyapunov function general functional response maturation delay Consumer-resource model

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