Effect of time delay on a detritus-based ecosystem

Gazi, Nurul Huda; Bandyopadhyay, Malay

doi:https://doi.org/10.1155/IJMMS/2006/25619

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 025619 | https://doi.org/10.1155/IJMMS/2006/25619

Effect of time delay on a detritus-based ecosystem

Nurul Huda Gazi¹and Malay Bandyopadhyay²

Received22 Apr 2005

Revised15 Jul 2006

Accepted18 Jul 2006

Published09 Oct 2006

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.

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Copyright © 2006 Hindawi Publishing Corporation. 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.

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