Hopf bifurcations in a predator-prey system of population allelopathy with a discrete delay and a distributed delay

DOI10.1007/s11071-012-0416-0zbMath1263.34070OpenAlexW1975634848WikidataQ115603346 ScholiaQ115603346MaRDI QIDQ1952360

Haihong Liu, Xinhui Wang, Chenglin Xu

Publication date: 30 May 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0416-0

zbMATH Keywords

stabilityperiodic solutionHopf bifurcationdistributed delaydiscrete delayLotka-Volterra predator-prey system

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Numerical methods for ordinary differential equations (65L99)

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Cites Work

• Unnamed Item
• Unnamed Item
• Bifurcations in a predator-prey model with discrete and distributed time delay
• A delayed predator-prey model with strong Allee effect in prey population growth
• Local Hopf bifurcation and global periodic solutions in a delayed predator--prey system
• Hopf bifurcations in a predator-prey system with a discrete delay and a distributed delay
• Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure
• Stability and Hopf bifurcation in a delayed predator-prey system with stage structure for prey
• Theory of functional differential equations. 2nd ed
• Global stability for two-species Lotka-Volterra systems with delay
• Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays
• Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays
• Theory and applications of partial functional differential equations
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• Stability and delays in a predator-prey system
• The study of a ratio-dependent predator-prey model with stage structure in the prey
• Bifurcation and stability analysis in predator-prey model with a stage-structure for predator
• Bifurcation analysis in a delayed Lotka-Volterra predator-prey model with two delays
• Hopf bifurcation in a delayed Lotka-Volterra predator-prey system
• Bifurcation analysis in a predator\,-\,prey system with time delay
• Hopf bifurcation and global periodic solutions in a delayed predator -- prey system
• Stability and bifurcation analysis for a delayed Lotka--Volterra predator--prey system
• Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays
• Stability and bifurcation for a delayed predator-prey model and the effect of diffusion

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