Nonlinear Phenomena in Complex Systems, 2002, Vol.5, No.1, pp.33-38

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2002, Vol.5, No.1, pp.33-38

Qualitative Analysis of a Resource - Based Autotroph - Herbivore Model with Delayed Nutrient Cycling
Kalyan Das and A.K. Sarkar

In this paper we consider a mathematical model of a resource based autotroph - herbivore system with a discrete delayed nutrient recycling. We have studied the growth of autotroph and herbivore population depending on the limiting nutrient which is partially recycled through decomposition. It has been shown that the supply rate of external resources plays the important role in shaping the dynamics of the autotroph-herbivore system. We have derived the conditions for asymptotic stability and switching to instability of the steady state. The length of the delay preserving the stability has also been derived.
Key words: autotroph - herbivore system, recycling, time-lag, stability, instability

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