A diffusive competition model with a protection zone

DOI10.1016/j.jde.2007.10.005zbMath1138.35039OpenAlexW2019149763MaRDI QIDQ2466488

Yihong Du, Xing Liang

Publication date: 15 January 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.10.005

zbMATH Keywords

spatial heterogeneityKrein-Rutman theoremmonotone dynamical systemHopf boundary lemma

Mathematics Subject Classification ID

Related Items (41)

Survival analysis of a single-species population model with fluctuations and migrations between patches ⋮ Combined effects of the spatial heterogeneity and the functional response ⋮ Spatial degeneracy vs functional response ⋮ Dynamics of Holling-type II prey–predator system with a protection zone for prey ⋮ The effect of protection zone on asymptotic dynamics of a reaction-diffusion model with a free boundary or unbounded boundary ⋮ Effect of cross-diffusion on the stationary problem of a Leslie prey-predator model with a protection zone ⋮ Dynamics of a diffusive prey-predator system with strong Allee effect growth rate and a protection zone for the prey ⋮ Asymptotic behavior of solutions of a reaction-diffusion model with a protection zone and a free boundary ⋮ A diffusion-advection predator-prey model with a protection zone ⋮ The protection zone of biological population ⋮ Uniqueness and stability of positive solutions for a diffusive predator-prey model in heterogeneous environment ⋮ Long-time behavior of a reaction-diffusion model with strong Allee effect and free boundary: effect of protection zone ⋮ Enhancing population persistence by a protection zone in a reaction-diffusion model with strong Allee effect ⋮ Effects of B-D functional response and protection zone on a predator-prey model ⋮ Necessary and sufficient conditions for existence of blow‐up solutions for elliptic problems in Orlicz–Sobolev spaces ⋮ Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone ⋮ Fish-hook shaped global bifurcation branch of a spatially heterogeneous cooperative system with cross-diffusion ⋮ Stationary patterns of a prey-predator system with a protection zone and cross-diffusion of fractional type ⋮ Effect of cross-diffusion in the diffusion prey-predator model with a protection zone. II ⋮ Positive steady states of the S-K-T competition model with spatially heterogeneous interactions ⋮ Uniqueness and non-uniqueness of steady states for a diffusive predator-prey-mutualist model with a protection zone ⋮ A robustness analysis of biological population models with protection zone ⋮ Protection Zones for Survival of Species in Random Environment ⋮ The role of protection zone on species spreading governed by a reaction-diffusion model with strong Allee effect ⋮ Effect of the protection zone on coexistence of the species for a ratio-dependent predator-prey model ⋮ Positive solutions for Lotka-Volterra competition system with large cross-diffusion in a spatially heterogeneous environment ⋮ Uniqueness and global stability of positive stationary solution for a predator-prey system ⋮ Effect of harvesting quota and protection zone in a reaction-diffusion model arising from fishery management ⋮ Effect of cross-diffusion in the diffusion prey-predator model with a protection zone ⋮ Unbounded connected component of the positive solution set of nonlinear operator equation and its applications ⋮ The protection zone for biological population in random environment ⋮ Protection zone in a diffusive predator-prey model with Beddington-DeAngelis functional response ⋮ Bifurcation analysis and dynamic behavior to a predator-prey model with Beddington-DeAngelis functional response and protection zone ⋮ A prey-predator model with harvesting for fishery resource with reserve area ⋮ Uniqueness and multiplicity of positive solutions for a diffusive predator–prey model in the heterogeneous environment ⋮ Effect of a protection zone in the diffusive Leslie predator-prey model ⋮ Effects of protection zone and nonlinear growth on a predator-prey model ⋮ Effects of dispersal for a predator-prey model in a heterogeneous environment ⋮ The role of strong Allee effect and protection zone on a diffusive prey-predator model ⋮ The effects of diffusion on the dynamics of a Lotka-Volterra predator-prey model with a protection zone ⋮ Protection zone in a modified Lotka-Volterra model

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