2001, Volume 4, Number 4, pp.406-411
In this paper we consider a mathematical model of
non-interactive type
autotroph-herbivore system. In the model equation we incorporated
discrete time delay in the specific
growth rate of autotroph and in the gestation term of herbivore. The
amount of autotroph biomass consumed by the herbivore is assumed
to follow
Holling type-II functional form. We have derived the conditions for local
and global
asymtotic stability of the steady state of the model system. The length
of the delay preserving the stability has also been derived.
The condition for existence of supercritical
Hopf-bifurcation are also derived. Lastly, the results have been
interpreted ecologically
Key words: Autotroph-herbivore system, gestation period,
time delay, stability, instability, supercritical Hopf-bifurcation
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