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Codimension two bifurcations in a predator-prey system with group defense. (English) Zbl 1091.92504
Summary: We study the qualitative behavior of a predator-prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including a saddle-node bifurcation, a supercritical Hopf bifurcation, and a 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.

MSC:
92D40Ecology
34C23Bifurcation (ODE)
34C60Qualitative investigation and simulation of models (ODE)
37N25Dynamical systems in biology