Dynamical complexity of a ratio-dependent predator-prey model with strong additive allee effect

Abstract

In this paper, a predator-prey systems of two species is proposed where prey population is subjected to a strong additive Allee effect and predator population consumes the prey according to the ratio-dependent Holling type-II functional response.We use the blow-up technique in order to explore the local structure of orbits in the vicinity of origin. We have determined the conditions for extinction/survival scenarios of species. Some basic dynamical results; the stability; phenomenon of bi-stability and the existence of separatrix curves; Hopf bifurcation; saddle-node bifurcation; homoclinic bifurcation, and Bogdanov-Takens bifurcation of the system are studied. Numerical simulation results that complement the theoretical predictions are presented. A discussion of the consequences of additive Allee effect on the model along with the ecological implications of the analytic and numerical findings is presented.