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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1453-1464 |
| Number of pages | 12 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 67 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 26 2007 |
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Keywords
- Bifurcation
- Heteroclinic cycle
- Ratio-dependent predator-prey model
ASJC Scopus subject areas
- Applied Mathematics