STATIONARY PATTERNS FOR A PREDATOR-PREY MODEL WITH HOLLING TYPE Ⅲ RESPONSE FUNCTION AND CROSS-DIFFUSION
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This paper deals with a predator-prey model with Holling type Ⅲ response function and cross-diffusion subject to the homogeneous Neumann boundary condition. We first give a priori estimates (positive upper and lower bounds) of positive steady states. Then the non-existence and existence results of non-constant positive steady states are given as the cross-diffusion coefficient is varied, which means that stationary patterns arise from cross-diffusion.
Abstract
This paper deals with a predator-prey model with Holling type Ⅲ response function and cross-diffusion subject to the homogeneous Neumann boundary condition. We first give a priori estimates (positive upper and lower bounds) of positive steady states. Then the non-existence and existence results of non-constant positive steady states are given as the cross-diffusion coefficient is varied, which means that stationary patterns arise from cross-diffusion.
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