We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.
WU, RUIWEN and LIU, XIUXAING
"Dynamics of a predator-prey system with a mate-finding Allee effect on prey,"
Turkish Journal of Mathematics: Vol. 41:
3, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/11