Wonlyul Ko

Coexistence of a one-prey two-predators model with ratio-dependent functional responses

Abstract We examine the positive coexistence of one prey and two competing predators in an interacting system with ratio-dependent functional responses under a hostile environment. Furthermore, we examine the extinction conditions for all three interacting species and for one or two of the three species. In addition, we present the biological interpretation and simulations based on the result. The methods employed are a comparison argument for the elliptic problem and the fixed-point theory applied to a positive cone on a Banach space.

On a predator-prey system with cross-diffusion representing the tendency of prey to keep away from its predators

Abstract In this work, we study a predator–prey system with cross-diffusion, representing the tendency of prey to keep away from its predators, under the homogeneous Dirichlet boundary condition. Using fixed point index theory, we provide some sufficient conditions for the existence of positive steady-state solutions. Furthermore, we investigate the non-existence of positive solutions.

POSITIVE COEXISTENCE FOR A SIMPLE FOOD CHAIN MODEL WITH RATIO-DEPENDENT FUNCTIONAL RESPONSE AND CROSS-DIFFUSION

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-difiusion is dis- cussed. Especially, when a cross-difiusion is small enough, the exis- tence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross- difiusion is su-ciently large, the extinction of prey species with cross-difiusion interaction to predator occurs. The method em- ployed is the comparison argument for elliptic problem and flxed point theory in a positive cone on a Banach space.

UNIQUENESS OF POSITIVE STEADY STATES FOR WEAK COMPETITION MODELS WITH SELF-CROSS DIFFUSIONS

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.