Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey.

*(English)*Zbl 1231.34021Summary: We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.

##### Keywords:

stage-structured; impulsive stocking; continuous harvesting; global attractivity; permanence
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\textit{J.-J. Jiao} et al., Appl. Math. Mech., Engl. Ed. 29, No. 5, 653--663 (2008; Zbl 1231.34021)

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