Persistence and extinction in three species Lotka-Volterra competitive systems

DOI10.1016/0025-5564(79)90018-XzbMath0413.92013OpenAlexW2065321263WikidataQ114684969 ScholiaQ114684969MaRDI QIDQ599021

Thomas C. Gard, Linda J. Svoboda, Thomas G. Hallam

Publication date: 1979

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(79)90018-x

zbMATH Keywords

stabilitynonlinear differential equationspersistenceextinctionfood webthree species Lotka-Volterra competitive system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Population dynamics (general) (92D25) Ecology (92D40) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (29)

Periodic competitive differential equations and the discrete dynamics of competitive maps ⋮ Permanence in Lotka-Volterra equations: Linked prey-predator systems ⋮ Persistence in three-dimensional Lotka-Volterra systems ⋮ Almost necessary and sufficient conditions for survival of species ⋮ An \(N\)-barrier maximum principle for elliptic systems arising from the study of traveling waves in reaction-diffusion systems ⋮ Semi-exact equilibrium solutions for three-species competition-diffusion systems ⋮ Dynamics of a stochastic three-species competitive model with Lévy jumps ⋮ N-barrier maximum principle for degenerate elliptic systems and its application ⋮ Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment ⋮ Dynamical behavior of a one-prey two-predator model with random perturbations ⋮ Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka–Volterra system of three competing species ⋮ Uniform persistence and global stability of two prey-predator pairs linked by competition ⋮ Survival and extinction in competitive systems ⋮ Quasisolutions and global attractor of reaction-diffusion systems ⋮ Stochastic three species systems ⋮ Time delays in n-species competition – I: Global stability in constant environments ⋮ Global asymptotic stability of non-negative steady states in, model ecosystems—I† ⋮ Partial persistence and extinction in \(N\)-dimensional competitive systems ⋮ Extinction in Competitive Lotka-Volterra Systems ⋮ Average growth and total permanence in a competitive Lotka-Volterra System ⋮ Global attractors in competitive systems ⋮ Dynamics of Lotka-Volterra competition reaction-diffusion systems with degenerate diffusion ⋮ Permanence of some ecological systems with several predator and one prey species ⋮ The persistence and stability for a predator-parasite-pest system ⋮ Global asymptotic stability in Volterra's population systems ⋮ Persistence and extinction in Lotka-Volterra reaction-diffusion equations ⋮ Persistence in periodic and almost periodic Lotka-Volterra systems ⋮ Nonlinear models for the survival of two competing species dependent on resource in industrial environments ⋮ Persistence in a model of three competitive populations

Cites Work

• Persistence in food webs - I. Lotka-Volterra food chains
• Nonlinear Aspects of Competition Between Three Species

This page was built for publication: Persistence and extinction in three species Lotka-Volterra competitive systems