International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 25619, 28 pages
doi:10.1155/IJMMS/2006/25619
Effect of time delay on a detritus-based ecosystem
1Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700 009, India
2Department of Mathematics, Scottish Church College, Kolkata 700 006, India
Received 22 April 2005; Revised 15 July 2006; Accepted 18 July 2006
Copyright © 2006 Nurul Huda Gazi and Malay Bandyopadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Models of detritus-based ecosystems with delay have received a
great deal of attention for the last few decades. This paper deals
with the dynamical analysis of a nonlinear model of a
detritus-based ecosystem involving detritivores and predator of
detritivores. We have obtained the criteria for local stability of
various equilibrium points and persistence of the model system.
Next, we have introduced discrete time delay due to recycling of
dead organic matters and gestation of nutrients to the growth
equations of various trophic levels. With delay differential
equation model system we have studied the effect of time delay on
the stability behaviour. Next, we have obtained an estimate for
the length of time delay to preserve the stability of the model
system. Finally, the existence of Hopf-bifurcating small amplitude
periodic solutions is derived by considering time delay as a
bifurcation parameter.