Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions

DOI10.1016/0167-2789(84)90002-2zbMath0588.35050OpenAlexW1963976531MaRDI QIDQ1073263

Masayuki Ito

Publication date: 1984

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(84)90002-2

zbMATH Keywords

bifurcation theoryequilibrium solutionslinearized stability analysisLotka-Volterra dynamicsinteraction coefficientscoupled pair of diffusion equationspositive stationary solutions

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Boundary value problems for nonlinear higher-order PDEs (35G30) Initial value problems for linear higher-order PDEs (35G10) Bifurcations in context of PDEs (35B32) Higher-order parabolic equations (35K25)

Related Items (12)

Coexistence regions in Lotka-Volterra models with diffusion ⋮ Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model ⋮ Bifurcation analysis of coexistent state in a delayed two-species predator-prey model ⋮ Coexistence-equilibria for competition-diffusion systems with a small diffusion rate ⋮ Comparison and numerical simulations for diffusive models of resource and sexual competition ⋮ Uniqueness and stability for coexistence solutions of the unstirred chemostat model ⋮ Uniqueness and stability of a predator-prey model with C-M functional response ⋮ A competition model for two resources in un-stirred chemostat ⋮ Bifurcation and stability of a two-species reaction-diffusion-advection competition model ⋮ Models for the effects of individual size and spatial scale on competition between species in heterogeneous environments ⋮ Bifurcation and stability of a two-species diffusive Lotka-Volterra model ⋮ Bifurcation from a double eigenvalue in the unstirred chemostat

Cites Work

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• Reaction-diffusion equations for competing species singularly perturbed by a small diffusion rate
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• Competition systems with Dirichlet boundary conditions
• Phase-plane solutions to some singular perturbation problems
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Nonlinear problems in the physical sciences and biology. Proceedings of a Battelle Summer Institute, Seattle, July 3-28, 1972
• Asymptotic behavior of a competition—diffusion system in population dynamics

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