Models for Single Species with Three Life History Stages and Cannibalism

( views:150, downloads:0 )
GAO Shu-jing()
Journal Title:
Volume 20, Issue 04, 2005
Key Word:
Stage structure;Time delay;Cannibalism;Global asymptotic stability

Abstract´╝Ü In this paper, single species models with three life history stages and cannibalism are investigated and analyzed. The main purpose of this paper is to study the effect of time delay on population growth. For the model without time delay, by using Liapunov functions, we obtain the equilibria of the system are globally asymptotically stable. For the model with time delay, it is shown that for some parameter values, the stability of the positive equilibrium can change a finite number of times at most as time delay is increased, and eventually it becomes unstable; but for other parameter values, the stability of the positive equilibrium does not change as time delay is increased. Numerical simulation is then presented.

  • [1]Aiello W G,Freedman H I.A time-delay model of single-species growth with stage structure[J].Math Biosci,1990,101(2):139-153.
  • [2]Wang Wendi,Ma Zhien.Harmless delays for uniform persistence[J].Journal of Mathematical Analysis and Applications,1998,158(1):256-268.
  • [3]Song X,Chen L.Modelling and analysis of a single species system with stage structure and harvesting[J].Math Comput Modelling,2002,36(1):67-82.
  • [4]Kuang Y.Delay Differential Equation with Application in Population Dynamics[M].New York:Academic Press,1993,78-82.
  • [5]Freedman H I,Wu J H.Periodic solutions of single-species models with periodic delay[J].SIAM J Anal,1992,23(3):689-701.
  • [6]Wang W D,Chen L S.A predator-prey system with stage-structure for predator[J].Comp Math Appl,1997,33(8):83-91.
WanfangData CO.,Ltd All Rights Reserved
About WanfangData | Contact US
Healthcare Department, Fuxing Road NO.15, Haidian District Beijing, 100038 P.R.China
Tel:+86-010-58882616 Fax:+86-010-58882615