Dynamics of the lotka-volterra systems with diffusion

DOI10.1080/00036819208840078zbMath0772.35028OpenAlexW1977890851MaRDI QIDQ4006081

Philip Korman

Publication date: 26 September 1992

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: http://purl.umn.edu/5177

zbMATH Keywords

long-time behaviorsteady statescooperating species caseevolution of population densitiesinteraction of two species

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Nonlinear elliptic equations (35J60) Ecology (92D40)

Related Items (15)

On the dynamics of two classes of periodic ecological models ⋮ Periodicity and blowup in a two-species cooperating model ⋮ Hopf bifurcation analysis in a diffusive predator-prey system with spatial heterogeneity and delays ⋮ Coexistence of three species in a strongly coupled elliptic system. ⋮ Coexistence in the three species predator--prey model with diffusion ⋮ On the symbiotic Lotka-Volterra model with diffusion and transport effects ⋮ Blow-up in a three-species cooperating model ⋮ Stability of synchronized steady state solution of diffusive Lotka-Volterra predator-prey model ⋮ Positive solutions for a modified Leslie-Gower prey-predator model with Crowley-Martin functional responses ⋮ The existence, bifurcation and stability of positive stationary solutions of a diffusive Leslie-Gower predator-prey model with Holling-type II functional responses ⋮ Coexistence states for systems of mutualist species ⋮ Coexistence of a general elliptic system in population dynamics ⋮ On diffusion-induced blowups in a mutualistic model ⋮ Domain synchronization of a cyclic Lotka-Volterra reaction diffusion mechanism ⋮ Stability and uniqueness for cooperative degenerate Lotka-Volterra model

Cites Work

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• Asymptotic behavior and stability of solutions of semilinear diffusion equations
• Invariant sets and existence theorems for semilinear parabolic and elliptic systems
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• Complicated dynamics of scalar reaction diffusion equations with a nonlocal term
• On the dirichlet problem for elliptic systems
• A general monotone scheme for elliptic systems with applications to ecological models
• On the existence and uniqueness of positive steady states in the volterra-lotka ecological models with diffusion
• On the Existence and Uniqueness of Positive Solutions for Competing Species Models with Diffusion

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