Rocky Mountain Journal of Mathematics

Global Stability and Hopf Bifurcation on a Predator-Prey System with Diffusion and Delays

Yuquan Wang

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 38, Number 5 (2008), 1685-1703.

Dates
First available in Project Euclid: 22 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1222088611

Digital Object Identifier
doi:10.1216/RMJ-2008-38-5-1685

Mathematical Reviews number (MathSciNet)
MR2457382

Zentralblatt MATH identifier
1176.34104

Subjects
Primary: 34C25: Periodic solutions 34K15 92D25: Population dynamics (general)

Keywords
Holling II functional response delay permanence global stability Hopf bifurcation

Citation

Wang, Yuquan. Global Stability and Hopf Bifurcation on a Predator-Prey System with Diffusion and Delays. Rocky Mountain J. Math. 38 (2008), no. 5, 1685--1703. doi:10.1216/RMJ-2008-38-5-1685. https://projecteuclid.org/euclid.rmjm/1222088611


Export citation

References

  • J.A. Cui, Permanence and periodic solution of Lotka-Volterra system with time delay Acta Math. Sinica 47 (2004), 512-520 (in Chinese).
  • --------, Permanence of predator-prey system with dispersal and time delay, Acta Math. Sinica 48 (2005), 479-488 (in Chinese).
  • K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic, Dordrecht, 1992%, 1-20.
  • Z.J. Gui and W.G. Ge, Permanence and stability for predator-prey system with diffusion and time delay J. Sys. Sci. Math. Sci. 25 (2005), 50-62 (in Chinese).
  • Y. Kuang and Y. Takeuchi, Predator prey dynamics in models of prey dispersal in two patch enviroments, Math. Biosci. 120 (1994), 77-98.
  • M.C. Luo and Z.E. Ma, The persistence of two species Lotka-Volterra model with diffusion, J. Biomath. 12 (1997), 52-59 (in Chinese).
  • X. Song and L.S. Chen, Periodic and global stability for nonautonomous predator-prey system with diffusion and time delay, Computers Math. Appl. 35 (1988), 33-40.
  • Y.L. Song, M.A. Han and J.J. Wei, Stability and global Hopf bifurcation for a predator-prey model with two delays, Chinese Ann. Math. 25 (2004), 783-790.
  • Y. Takeuchi, Global stability in generalized Lotka -Volterra diffusion system, J. Math. Appl. 16 (1986), 209-221.
  • --------, Diffusion effect on stability of Lotka-Volterra models of prey dispersal in two patchs enviroments, Math. Biosci. 120 (1994), 77-98.
  • Y.Q. Wang and Z.J. Jing, Qlobal qualitative analysis of a food chain model, Acta Math. Sci. 26 (2006), 410-420 (in Chinese).
  • Y.Q. Wang, Z.J. Jing and K.Y. Chen, Multiple limit cycles and global stability in predator-prey model, Acta Math. Appl. Sinica 15 (1999), 206-219.
  • X.A. Zhang, Z.J. Liang and L.S. Chen, The dispersal properties of a class of predator-prey LV model, J. Sys. Sci. Math. Sci. 19 (1999), 407-414 (in Chinese).