Stability of a stage-structured predator-prey model with Allee effect and harvesting

Abstract

A stage-structured predator-prey model with Allee effect on predator species and harvesting on prey species is introduced and studied. The local stability of the positive equilibrium is discussed by the sign of eigenvalue. Furthermore, by using the iterative method, some suitable sufficient conditions for the global attractivity of the equilibria are obtained. Our results show that the Allee effect has no influence on the local stability and global attractivity of the interior equilibrium, such a result is different from the known results. Furthermore, numeric simulations show the interior equilibrium spends a much longer time to achieve the stable state due to the Allee effect.