World Academy of Science, Engineering and Technology
Published September 6, 2013 | Version 16966
Journal article Open

Periodic Orbits in a Delayed Nicholson's Blowflies Model

Authors/Creators

Description

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out.

Files

16966.pdf

Files (151.9 kB)

Name Size Download all
md5:1d3000e422560c6a49195eb1801bf4b6
151.9 kB Preview Download

Additional details

References

  • <p>
  • Y. Kuang, Delay Differential Equations with Applications in Population Dynamics. Academic Press, INC, 1993.
  • J. Hale,Theory of Functional Differential Equations. Springer-Verlag, 1977.
  • M. Kot, Elements of Mathematical Ecology. Cambridge University Press, 2001.
  • A.J. Nicholson, An outline of the dynamics of animal populations, Aust. J. Zool. 2(1954) 9-65.
  • W.S.C. Gurney, S.P. Blythe, R.M. Nisbet, Nicholson,s blowflies revisited. Nature 287(1980)17-21.
  • S.H. Saker, B.G. Zhang, Oscillation in a discrete partial delay Nicholsons blowflies model. Math. Comput. Modelling 36 (9-10) (2002) 1021-1026.
  • J.W. Li, C.X. Du, Existence of positive periodic solutions for a generalized Nicholsons blowflies model. J. Comput. Appl. Math. 221 (1) (2008) 226-233.
  • W.T. Li, Y.H. Fan, Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholsons blowflies model. J. Comput. Appl. Math. 201 (1) (2007) 55-68.
  • B.G. Zhang, H.X. Xu, A note on the global attractivity of a discrete model of nicholsons blowflies. Discrete Dyn. Nat. Soc. 3 (1999) 51-55. [10] J.J.Wei, Michael Y. Li, Hopf bifurcation analysis in a delayed Nicholson blowflies equation. Nonlinear Anal. 60 (7) (2005) 1351-1367. [11] S.H. Saker, S. Agarwal, Oscillation and global attractivity in a periodic Nicholsons blowflies model. Math. Comput. Modelling 35 (2002) 719- 731. [12] L. Berezansky, E. Braverman, L. Idels, Nicholson,s blowflies differential equations revisited: main results and open problems. Appl. Math. Modelling 34 (2010) 1405-1417.</p>