An interfacial approach to regional segregation of two competing species mediated by a predator

DOI10.1007/BF00166143zbMath0774.92023OpenAlexW2060424841WikidataQ115610767 ScholiaQ115610767MaRDI QIDQ1802937

Masayasu Mimura, Tsutomu Ikeda

Publication date: 29 June 1993

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00166143

zbMATH Keywords

interface equationpredator-prey modelLotka-Volterra interactioninternal layercoexistence of two competing speciesdynamics of spatial segregationinterfacial dynamics approachperiodic and chaotic dynamicspredation-mediated coexistence

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Ecology (92D40) Dynamical systems and ergodic theory (37-XX)

Related Items (14)

Strategy and stationary pattern in a three-species predator--prey model ⋮ Dynamical transition for a 3-component Lotka-Volterra model with diffusion ⋮ Stationary patterns for a prey-predator model with prey-dependent and ratio-dependent functional responses and diffusion ⋮ The formation of spreading front: the singular limit of three-component reaction-diffusion models ⋮ Positive solutions for a three-trophic food chain model with diffusion and Beddington-DeAngelis functional response ⋮ Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems ⋮ Contracting sets and dissipation ⋮ Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model ⋮ Coexistence of a three species predator-prey model with diffusion and density dependent mortality ⋮ Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion ⋮ Stationary patterns caused by cross-diffusion for a three-species prey-predator model ⋮ Stationary patterns of strongly coupled prey--predator models ⋮ Qualitative analysis of the Oregonator model ⋮ Qualitative analysis of predator-prey models with Beddington-De Angelis functional response and diffusion

Cites Work

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• Existence and bifurcation of stable equilibrium in two-prey, one-predator communities
• Pattern formation in competition-diffusion systems in nonconvex domains
• The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• The heat equation shrinks embedded plane curves to round points
• Predator-mediated coexistence and extinction
• Dynamics of interfaces in reaction diffusion systems
• Instability and Turbulence of Wavefronts in Reaction-Diffusion Systems
• Euclidean Invariant Formulation of Phase Dynamics. I: Non-Propagating Periodic Pattern
• Layer Oscillations in Reaction-Diffusion Systems
• Stability of Singularly Perturbed Solutions to Systems of Reaction-Diffusion Equations

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