آمار
| تعداد نشریات | 26 |
| تعداد شمارهها | 447 |
| تعداد مقالات | 4,557 |
| تعداد مشاهده مقاله | 5,380,003 |
| تعداد دریافت فایل اصل مقاله | 3,580,072 |
BIFURCATION ANALYSIS OF A DDE MODEL OF THE CORAL REEF | ||
| Journal of Mahani Mathematical Research | ||
| مقاله 2، دوره 5، شماره 1، فروردین 2016، صفحه 9-25 اصل مقاله (202.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2017.1555 | ||
| نویسندگان | ||
| HANIYEH FATTAHPOUR؛ HAMID R. Z. ZANGENEH* | ||
| DEPARTMENT OF MATHEMATICAL SCIENCES, ISFAHAN UNIVERSITY OF TECHNOLOGY, ISFAHAN, IRAN, 84156-83111 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Ordinary differential equation؛ Delay differential equation؛ Stability؛ Hopf bifurcation؛ periodic solution | ||
|
آمار تعداد مشاهده مقاله: 1,093 تعداد دریافت فایل اصل مقاله: 1,298 |
||