Name
Title | ||
|---|---|---|
Heteroclinic Bifurcation in the Michaelis-Menten-Type Ratio-Dependent Predator-Prey System |
Abstract | ||
|---|---|---|
The existence of a heteroclinic bifurcation for the Michaelis-Menten-type ratio-dependent predator-prey system is rigorously established. Limit cycles related to the heteroclinic bifurcation are also discussed. It is shown that the heteroclinic bifurcation is characterized by the collision of a stable limit cycle with the origin, and the bifurcation triggers a catastrophic shift from the state of large oscillations of predator and prey populations to the state of extinction of both populations. It is also shown that the limit cycles related to the heteroclinic bifurcation originally bifurcate from the Hopf bifurcation. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/060662460 | SIAM JOURNAL ON APPLIED MATHEMATICS |
Keywords | Field | DocType |
ratio-dependent predator-prey model,heteroclinic cycle,bifurcation | Bogdanov–Takens bifurcation,Biological applications of bifurcation theory,Heteroclinic cycle,Mathematical analysis,Bifurcation diagram,Heteroclinic bifurcation,Transcritical bifurcation,Pitchfork bifurcation,Saddle-node bifurcation,Mathematics | Journal |
Volume | Issue | ISSN |
67 | 5 | 0036-1399 |
Citations | PageRank | References |
5 | 0.92 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bingtuan Li | 1 | 35 | 9.86 |
| Yang Kuang | 2 | 33 | 22.07 |