Stability and Bifurcation Analysis in a Delayed Predator-Prey System with Mate-Finding Allee Effect

The stability and bifurcation analysis of a delayed ratio-dependent predator-prey system with a mate-finding Allee effect on prey is discussed. The delay is chosen as the bifurcation parameter and the system may experience ~Hopf~ bifurcation. Moreover, our results show that under some conditions the system has a Bogdanov-Takens singularity, which indicates that the delay has an important effect on the dynamical behaviors of the system.