Nonlinear Phenomena in Complex Systems, 2004, Vol.7, No.3, pp.238-249

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2004, Vol.7, No.3, pp.238-249

Global Stability and Bifurcation in a Delayed Nonlinear Autotroph-Herbivore Model.
M. Bandyopadhyay

The main objective of the paper is to study the effect of time-delay on dynamics of the autotroph-herbivore system. This consists of three parts. The first deals with a brief introduction of the autotroph-herbivore model system in presence of gestation delay. In the second part we have tried to find out the parametric conditions under which the delay has no ability to change the stability properties of the model system. In the third and final part we have investigated the conditions for global stability and hence the uniform persistence to hold for the model system under consideration.
Key words: autotroph - herbivore, bifurcation, gestation delay, stability, global stability, uniform persistence

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