Bifurcation analysis of a detritus-based ecosystem with time delay. (English) Zbl 1009.92036
Summary: This article concentrates on the study of delay effects of a mangrove ecosystem of detritus, detritivores and predators of detritivores. Local stability criteria are derived in the absence of delays. Conditions are found for which the system undergoes a Hopf bifurcation. Further conditions are derived for which there can be no change in stability.
MSC:
| 92D40 | Ecology |
| 34K18 | Bifurcation theory of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
References:
| [1] | DOI: 10.1016/0022-0981(93)90250-R · doi:10.1016/0022-0981(93)90250-R |
| [2] | DOI: 10.1016/0022-0981(95)00159-X · doi:10.1016/0022-0981(95)00159-X |
| [3] | DOI: 10.1017/S0007485300055826 · doi:10.1017/S0007485300055826 |
| [4] | DOI: 10.1017/S0007485300003813 · doi:10.1017/S0007485300003813 |
| [5] | Ray S., Current Sci. 57 pp 1120– (1988) |
| [6] | Ray S., Current Sci. 57 pp 159– (1988) |
| [7] | Ray S., J. Trop. Ecol. 30 pp 45– (1989) |
| [8] | Ray S., J. Biol. Syst. 8 pp 263– (2000) |
| [9] | Steinke T. D., S. Afr. J. Bot. 54 pp 445– (1988) · doi:10.1016/S0254-6299(16)31276-5 |
| [10] | DOI: 10.1016/S0022-0981(97)00246-3 · doi:10.1016/S0022-0981(97)00246-3 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
