In this paper we study the qualitative behavior of a predator-prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the so-called "paradox of enrichment" phenomenon. In the generic case, the model has the bifurcation of cusp-type codimension two (i.e. the Bogdanov-Takens bifurcation) but no bifurcations of codimension three.
|Original language||English (US)|
|Number of pages||9|
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - 2001|
ASJC Scopus subject areas
- Applied Mathematics