Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction

Wonlyul Ko; Inkyung Ahn

doi:10.3934/cpaa.2018021

Article Contents

2018, Volume 17, Issue 2: 375-389. Doi: 10.3934/cpaa.2018021

This issue Previous Article Global existence and decay estimate of classical solutions to the compressible viscoelastic flows with self-gravitating Next Article The asymptotic limits of solutions to the Riemann problem for the scaled Leroux system

Pattern formation of a diffusive eco-epidemiological model with predator-prey interaction

Wonlyul Ko^1, and
Inkyung Ahn^2, ,

1.
Department of Mathematics, Korea University, Anam-dong, Seoul, 02841, South Korea
2.
Department of Mathematics, Korea University, Sejong-ro Sejong, 30019, South Korea

Received: January 31, 2017

Revised: July 31, 2017

Published: June 2018

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Abstract

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.

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Mathematics Subject Classification: Primary:35J60, 35K57;Secondary:35B36.

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References

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