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This is Part II of our study on the positive steady state of a quasi-linear reaction-diffusion system in one space dimension introduced by Klausmeier and Litchman for the modelling of the distributions of phytoplankton biomass and its nutrient. In Part I, we proved nearly optimal existence and nonexistence results. In Part II, we obtain complete… (More)

- Yihong Du, Junping Shi
- 2006

A spatially heterogeneous reaction-diffusion system modelling predator-prey interaction is studied, where the interaction is governed by a Holling type II functional response. Existence of multiple positive steady states and global bifurcation branch are examined as well as related dynamical behavior. It is found that while the predator population is not… (More)

- Yihong Du, Junping Shi
- 2005

We present several recent results obtained in our attempts to understand the influence of spatial heterogeneity in the predator-prey models. Two different approaches are taken. The first approach is based on the observation that the behavior of many diffusive population models is very sensitive to certain coefficient functions becoming small in part of the… (More)

- Yihong Du, Junping Shi, J Shi
- 2006

In this paper we study the effects of a protection zone Ω 0 for the prey on a diffusive predator–prey model with Holling type II response and no-flux boundary condition. We show the existence of a critical patch size described by the principal eigenvalue λ D 1 (Ω 0) of the Laplacian operator over Ω 0 with homogeneous Dirich-let boundary conditions. If the… (More)

In this paper we analyze a nonlocal reaction-diffusion model which arises from the modeling of competition of phytoplankton species with incomplete mixing in a water column. The nonlocal nonlinearity in the model describes the light limitation for the growth of the phy-toplankton species. We first consider the single species case and obtain a complete… (More)

We investigate, from a more ecological point of view, a free boundary model considered in [11] and [8] that describes the spreading of a new or invasive species, with the free boundary representing the spreading front. We derive the free boundary condition by considering a " population loss " at the spreading front, and correct some mistakes regarding the… (More)