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 - 2007 |
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Keywords
- Bifurcation
- Heteroclinic cycle
- Ratio-dependent predator-prey model
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Heteroclinic bifurcation in the Michaelis-Menten-type ratio-dependent predator-prey system. / Li, Bingtuan; Kuang, Yang.
In: SIAM Journal on Applied Mathematics, Vol. 67, No. 5, 2007, p. 1453-1464.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Heteroclinic bifurcation in the Michaelis-Menten-type ratio-dependent predator-prey system
AU - Li, Bingtuan
AU - Kuang, Yang
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Heteroclinic cycle
KW - Ratio-dependent predator-prey model
UR - http://www.scopus.com/inward/record.url?scp=35349008509&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=35349008509&partnerID=8YFLogxK
U2 - 10.1137/060662460
DO - 10.1137/060662460
M3 - Article
AN - SCOPUS:35349008509
VL - 67
SP - 1453
EP - 1464
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 5
ER -