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.
Highlights
In the classical predator-prey model, many scholars assumed that each prey species has the same fertility and survivability, but this is not realistic
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
It bring to our attention that to this day, still no scholar investigate the influence of the Allee effect on the stage structure model, since the creatures of higher rank are more likely to die out or have Allee effect, due to the lack of food, it is necessary to investigated the predator prey system incorporating Allee effect to predator species
Summary
In the classical predator-prey model, many scholars assumed that each prey species has the same fertility and survivability, but this is not realistic. Liu and Xie [7] argued that the higher the hierarchy in the food chain, the more likely it is to become extinct They proposed the following predator prey model with predator species subject to Allee effect: dx dy y. It bring to our attention that to this day, still no scholar investigate the influence of the Allee effect on the stage structure model, since the creatures of higher rank are more likely to die out or have Allee effect, due to the lack of food, it is necessary to investigated the predator prey system incorporating Allee effect to predator species. Base on the works of Song and Chen [2], we propose the stage-structured predator-prey model with Allee effect on predator species and harvesting on prey species.
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