GLOBAL STABILITY AND HOPF BIFURCATION IN A DELAYED DIFFUSIVE LESLIE–GOWER PREDATOR–PREY SYSTEM

DOI10.1142/S0218127412500617zbMath1270.35376OpenAlexW2108123681WikidataQ115523844 ScholiaQ115523844MaRDI QIDQ2843552

Junjie Wei, Junping Shi, Shanshan Chen

Publication date: 23 August 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127412500617

zbMATH Keywords

delayglobal stabilitypredator-preyHopf bifurcationreaction-diffusion

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Partial functional-differential equations (35R10) Bifurcations in context of PDEs (35B32)

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Cites Work

• Unnamed Item
• Harmless delays for permanence in a class of population models with diffusion effects
• Non-constant positive steady-states of a diffusive predator--prey system in homogeneous environment
• Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays
• Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model
• Asymptotic behavior of an SEI epidemic model with diffusion
• Asymptotic stability of positive equilibrium solution for a delayed prey-predator diffusion system
• Global stability of a reaction-diffusion predator-prey model with a nonlocal delay
• Stability and Hopf bifurcation for a delayed prey-predator system with diffusion effects
• Retracted: Stability and Hopf bifurcations in a delayed Leslie-Gower predator-prey system
• Convergence of solutions for Volterra-Lotka prey-predator systems with time delays
• Systems of parabolic equations with continuous and discrete delays
• A Lyapunov function for Leslie-Gower predator-prey models
• A diffusive predator-prey model in heterogeneous environment
• Dynamics of nonlinear parabolic systems with time delays
• Diffusion effect and stability analysis of a predator-prey system described by a delayed reaction-diffusion equations
• Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects
• The properties of a stochastic model for the predator-prey type of interaction between two species
• Bifurcation and stability analysis for a delayed Leslie-Gower predator-prey system
• On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
• Multiparameter Bifurcation of a Predator-Prey System
• Positive steady states of the Holling–Tanner prey–predator model with diffusion
• Global Stability for a Class of Predator-Prey Systems
• SOME FURTHER NOTES ON THE USE OF MATRICES IN POPULATION MATHEMATICS
• Stability and bifurcation for a delayed predator-prey model and the effect of diffusion
• A non-local delayed and diffusive predator-prey model.
• Convergence of solutions of reaction-diffusion systems with time delays