Nonlinear Phenomena in Complex Systems, 2001, Vol.4, No.4, pp.406-411

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 4, pp.406-411

Stability and Bifurcation of Two Interacting Species with Time Delay
Kalyan Das and A.K.Sarkar

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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