Stable oscillations in a predator-prey model with time lag

DOI10.1016/0022-247X(84)90211-7zbMath0536.92023WikidataQ115599959 ScholiaQ115599959MaRDI QIDQ5896307

Miklos Farkas

Publication date: 1984

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

center manifoldLotka-Volterra modelsupercritical Hopf bifurcationattractive closed orbitspredator-prey model with time lag

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Population dynamics (general) (92D25) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (17)

Degenerate Lyapunov functionals of a well-known prey–predator model with discrete delays ⋮ Multiparameter bifurcation diagrams in predator-prey models with time lag ⋮ Effects of dispersal in a tri-trophic metapopulation model ⋮ Dynamics and stability of two predators-one prey mathematical model with fading memory in one predator ⋮ Repellers in systems with infinite delay ⋮ Bifurcations and Dynamics in Modified Two Population Neuronal Network Models ⋮ Great delay in a predator-prey model ⋮ Stability and Hopf bifurcation of a mathematical model describing bacteria-fish interaction in marine environment ⋮ Bifurcations and chaos in a predator-prey model with delay and a laser-diode system with self-sustained pulsations. ⋮ Oscillatory Behavior of a Delayed Ratio-Dependent Predator–Prey System with Michaelis–Menten Functional Response ⋮ Stable oscillations in a predator-prey model with time lag ⋮ On bifurcations and chaos in predator-prey models with delay ⋮ Dynamics of predator-prey system with fading memory ⋮ A remark on M. Farkas: Stable oscillations in a predator-prey model with time lag ⋮ Stability switch and Hopf bifurcation for a diffusive prey-predator system with delay ⋮ Bifurcations in a predator-prey model with general logistic growth and exponential fading memory ⋮ Bifurcations in a predator-prey model with memory and diffusion. I: Andronov-Hopf bifurcation

Cites Work

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• Nonconstant periodic solutions in predator-prey systems with continuous time delay
• Time delay in prey-predator models
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Time delay in prey-predator models. II: Bifurcation theory
• On the nature of turbulence
• Global Stability in Ecological Systems with Continuous Time Delay
• Attractivity and Hopf bifurcation

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