TWO–PREDATOR AND TWO–PREY SPECIES GROUP DEFENCE MODEL WITH SWITCHING EFFECT

Qamar J.A. Khan, Edamana V. Krishnan, and Easwaran Balakrishnan

View Full Paper

References

  1. [1] C.S. Holling, Principles of insect predation, Annual Review of Entomology, 6, 1961, 163–182.
  2. [2] F. Takahashi, Reproduction curve with two equilibrium points: A consideration on the fluctuation of insect population, Research Population Ecology, 47, 1964, 733–745.
  3. [3] R.M. May, Some mathematical problems in biology, Vol. 4 (Providence, RI: American Mathematical Society, 1974).
  4. [4] W.W. Murdoch & A. Oaten, Predation and population stability, Advances in Ecology Research, 9, 1975, 1–31.
  5. [5] J. Roughgarden & M. Feldman, Species packing and predation pressure, Ecology, 56, 1975, 489–492.
  6. [6] M. Tansky, Progress in theoretical biology (Edited by R. Rosen), 4 (London: Academic Press, 1976).
  7. [7] M. Tansky, Switching effects in prey-predator system, Journal of Theoretical Biology, 70, 1978, 263–272.
  8. [8] R. Prajneshu & P. Holgate, A prey-predator model with switching effect, Journal of Theoretical Biology, 125, 1987, 61–66.
  9. [9] J.N. McNair, A reconcillation of simple and complex models of age – dependent predation, Theoretical Population Biology, 32, 1987, 383–392.
  10. [10] Q.J.A. Khan, B.S. Bhatt, & R.P. Jaju, Stability of a switching model with two habitats and a predator, Journal of the Physical Society Japan, 63, 1994, 1995–2001.
  11. [11] F. Courchamp, M. Langlais, & G. Sugihara, Rabbits killing birds: Modelling the hyperpredation process, Journal of Animal Ecology, 69, 2000, 154–164.
  12. [12] J. Zhang, M. Fan, & Y. Kuang, Rabbits killing birds revisited, Mathematical Biosciences, 203, 2006, 100–123.
  13. [13] J.S. Tener, Muskoxen, (Ottawa: Queen’s Printer, 1965).
  14. [14] R.D. Yang & A.F. Humphrey, Dynamics and steady state studies of phenol biodegeneration in pure and mixed cultures, Biotechnology and Bioengineering, 17, 1975, 1211–1235.
  15. [15] R.M. May & S.K. Robinson, Population dynamics of avian brood parasitism, American Naturalist, 126, 1985, 475–494.
  16. [16] H.I. Freedman & G.S.K. Walkowicz, Predator-prey system with group defense: The paradox of enrichment revisited, Bulletin of Mathematical Biology, 48, 1986, 493–508.
  17. [17] S. Ruan & H.I. Freedman, Persistence in three species food chain models with group defence, Mathematical Biosciences, 111, 1992, 73–87.
  18. [18] Q.J.A. Khan, B.S. Bhatt, & R.P. Jaju, Switching model with two habitats and a predator involving group defence, Journal of Nonlinear Mathematical Physical, 5, 1998, 212–229.
  19. [19] D. Mukherjee & A.B. Roy, Global stability of prey-predator systems with predatory switching, Biosystems, 27, 1992, 171– 178.
  20. [20] Q.J.A. Khan, E. Balakrishnan, & G.C. Wake, Analysis of a predator-prey system with predator switching, Bulletin of Mathematical Biology, 66, 2004, 109–123.

Important Links:

Go Back