Effect of time delay on a detritus-based ecosystem
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 loca...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/25619 |
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| _version_ | 1832561890557952000 |
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| author | Nurul Huda Gazi Malay Bandyopadhyay |
| author_facet | Nurul Huda Gazi Malay Bandyopadhyay |
| author_sort | Nurul Huda Gazi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-100fd93944cb480fafae11be36667e8f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-100fd93944cb480fafae11be36667e8f2025-02-03T01:23:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/2561925619Effect of time delay on a detritus-based ecosystemNurul Huda Gazi0Malay Bandyopadhyay1Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700 009, IndiaDepartment of Mathematics, Scottish Church College, Kolkata 700 006, IndiaModels 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.http://dx.doi.org/10.1155/IJMMS/2006/25619 |
| spellingShingle | Nurul Huda Gazi Malay Bandyopadhyay Effect of time delay on a detritus-based ecosystem International Journal of Mathematics and Mathematical Sciences |
| title | Effect of time delay on a detritus-based ecosystem |
| title_full | Effect of time delay on a detritus-based ecosystem |
| title_fullStr | Effect of time delay on a detritus-based ecosystem |
| title_full_unstemmed | Effect of time delay on a detritus-based ecosystem |
| title_short | Effect of time delay on a detritus-based ecosystem |
| title_sort | effect of time delay on a detritus based ecosystem |
| url | http://dx.doi.org/10.1155/IJMMS/2006/25619 |
| work_keys_str_mv | AT nurulhudagazi effectoftimedelayonadetritusbasedecosystem AT malaybandyopadhyay effectoftimedelayonadetritusbasedecosystem |