Abstract
A two-dimensional predator-prey model constructed in this article to study how the fear of predator on prey will reduce the intrinsic growth rate of prey. The Allee effect in prey population is included to describe the minimum requirement of the individual to achieve the positive growth of the prey population. Anti-predation and harvesting on the predator population are also considered in the model. We non-dimensionalized the model first before analyzing the existence and the local stability criteria of all equilibrium points. The analytical results showed how the harvesting intervention would determine the local stability criteria of the coexistence equilibrium point. We found that the time scale separation does not impact the stability of equilibrium points. Some numerical simulation is given to show how the system behaves depend on the periodic harvesting interventions.
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