Global bifurcation structure of positive stationary solutions for a classical Lotka-Volterra competition model with diffusion

DOI10.1007/BF03167424zbMath1050.35013MaRDI QIDQ1433506

Yukio Kan-On

Publication date: 18 June 2004

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

comparison principlepositive solutionLotka-Volterra systemsinterval arithmeticbifurcation theory

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Bifurcations in context of PDEs (35B32)

Related Items (4)

Bifurcation structure of positive stationary solutions for a Lotka-Volterra competition model with diffusion. I: Numerical verification of local structure ⋮ Structure of radially symmetric positive stationary solutions for a reaction-diffusion system with competitive interaction ⋮ A uniqueness theorem of radially symmetric positive stationary solutions for a competition-diffusion system ⋮ Shadow system approach to a plankton model generating harmful algal bloom

Cites Work

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• The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
• Geometric theory of semilinear parabolic equations
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• A note on the propagation speed of travelling waves for a Lotka-Volterra competition model with diffusion
• Stability of monotone travelling waves for competition-diffusion equations
• Existence of standing waves for competition-diffusion equations
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Bifurcation structure of stationary solutions of a Lotka--Volterra competition model with diffusion
• Parameter Dependence of Propagation Speed of Travelling Waves for Competition-Diffusion Equations

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