Global stability and oscillations in classical Lotka-Volterra loops

DOI10.1007/BF00275505zbMath0609.92032OpenAlexW2052985345WikidataQ113909311 ScholiaQ113909311MaRDI QIDQ1087501

Fortunata Solimano, A. B. Roy

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1007/bf00275505

zbMATH Keywords

stabilityglobal stabilityglobal boundednesspredator-prey systemLotka-Volterra model3-species cyclic loopacyclic loopsnonnegative and stable equilibriumsufficient conditions for global asymptotic stability

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Growth and boundedness of solutions to ordinary differential equations (34C11) Chemical kinetics in thermodynamics and heat transfer (80A30) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (10)

Limit cycles in a prey-predator system ⋮ Asymptotic behavior of quasi-competitive species defined by Lotka-Volterra dynamics ⋮ Permanence for three species with cyclic loop ⋮ Computer aided proof for the global stability of Lotka-Volterra systems ⋮ Dynamical behavior of a one-prey two-predator model with random perturbations ⋮ Stochastic three species systems ⋮ Effect of parity on productivity and sustainability of Lotka-Volterra food chains ⋮ Nonlinear state-dependent feedback control of a pest-natural enemy system ⋮ Hopf bifurcation and transition to chaos in Lotka-Volterra equation ⋮ Adiabatic invariants of slowly varying three-dimensional systems and the existence of invariant tori of the Lotka-Volterra equation

Cites Work

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• Topics in stability and bifurcation theory
• On $\omega $-Limits for Competition Between Three Species
• Global asymptotic stability for a class of many-variable volterra prey-predator systems
• Asymptotic Behaviors in the Dynamics of Competing Species

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