Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model

DOI10.3934/dcdsb.2014.19.747zbMath1291.37091OpenAlexW2329845971MaRDI QIDQ2438877

Xihui Lin, Michael Y. Li, Hao Wang

Publication date: 7 March 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.747

zbMATH Keywords

bifurcationlimit cycledelay differential equationpredator-prey modelstability switchglobal Hopf branch

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Asymptotic stability in control theory (93D20) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Bifurcation theory of functional-differential equations (34K18) General biology and biomathematics (92B05)

Related Items (8)

Refuge-mediated predator-prey dynamics and biomass pyramids ⋮ Delay induced stability switch, multitype bistability and chaos in an intraguild predation model ⋮ Dynamics of a predator-prey model with distributed delay to represent the conversion process or maturation ⋮ Dynamical analysis and consistent numerics for a delay model of viral infection in phytoplankton population ⋮ Delay induced multiple stability switch and chaos in a predator-prey model with fear effect ⋮ Chaotic dynamics in a simple predator-prey model with discrete delay ⋮ Analysis of a predator-prey model with distributed delay ⋮ \(R_0\) and sensitivity analysis of a predator-prey model with seasonality and maturation delay

Uses Software

• DDE-BIFTOOL

Cites Work

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• The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles
• Elements of applied bifurcation theory.
• Introduction to functional differential equations
• Stability and delays in a predator-prey system
• Global dynamics of Nicholson's blowflies equation revisited: onset and termination of nonlinear oscillations
• Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters

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