In this paper, first we discuss a local stability analysis of model was introduced by P. J. Mumby et. al. (2007), with $\frac{gM^{2}}{M+T}$ as the functional response term. We conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef. Next, we consider this model under the influence of the time delay as the bifurcation parameter. We show that for small time delay, the stability type of the equilibria will not change, however for large enough time delay, the interior equilibrium point become unstable in contrast to the ODE case. Also for some critical grazing intensity and the time delay, a Hopf bifurcation occur and a nontrivial periodic orbit will appear. Further we discuss its corresponding stability switching directions.
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SYSTEMS AND GEOMETRIC THEORIES, 11-12 DECEMBER 2016, MAHANI MATHEMATICAL RESEARCH CENTER, SHAHID BAHONAR UNIVERSITY OF KERMAN
FATTAHPOUR, H., & R. Z. ZANGENEH, H. (2017). BIFURCATION ANALYSIS OF A DDE MODEL OF THE CORAL REEF. Journal of Mahani Mathematical Research, 5(1), 9-25. doi: 10.22103/jmmrc.2017.1555
MLA
HANIYEH FATTAHPOUR; HAMID R. Z. ZANGENEH. "BIFURCATION ANALYSIS OF A DDE MODEL OF THE CORAL REEF", Journal of Mahani Mathematical Research, 5, 1, 2017, 9-25. doi: 10.22103/jmmrc.2017.1555
HARVARD
FATTAHPOUR, H., R. Z. ZANGENEH, H. (2017). 'BIFURCATION ANALYSIS OF A DDE MODEL OF THE CORAL REEF', Journal of Mahani Mathematical Research, 5(1), pp. 9-25. doi: 10.22103/jmmrc.2017.1555
VANCOUVER
FATTAHPOUR, H., R. Z. ZANGENEH, H. BIFURCATION ANALYSIS OF A DDE MODEL OF THE CORAL REEF. Journal of Mahani Mathematical Research, 2017; 5(1): 9-25. doi: 10.22103/jmmrc.2017.1555
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