Models for Single Species with Three Life History Stages and Cannibalism

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Author:
GAO Shu-jing()
Journal Title:
JOURNAL OF BIOMATHEMATICS
Issue:
Volume 20, Issue 04, 2005
DOI:
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.

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