The impact of additive Allee effect in a population system

  • Koushik Garain National Institute of Technology Patna, Patna, Bihar, India


Here a prey-predator model with Beddington-DeAangelis type functional response and density dependent death rate for predators is investigated. One crucial phenomenon additive Allee effect is included in this model. We investigate the complete global dynamics of the system, and for this, a two-parametric bifurcation diagram has been presented, which describes the effect of Allee effect and conversion rate. Dynamical properties of our model is very complicated, three Bogdanov-Takens bifurcation points and two Generalized hopf bifurcation points are observed. We have noticed through bifurcation study that the Allee effect enriches the dynamics of the system and increases the extinction risk of both the populations. It is also found that the equilibrium of the model could change from stable to unstable, and then to extinct when the strength of Allee effect increases continuously from zero and the same result will follow for conversion rate. We notice that density dependent rate of predator increases the number of interior equilibrium points. All possible bifurcations that the system could go
through have also been examined.