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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang, 550004, P. R. China

    Jian-jun Jiao  (焦建军)

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, P. R. China

    Jian-jun Jiao  (焦建军) & Lan-sun Chen  (陈兰荪)

  3. Department of Mathematical Analysis, Faculty of Mathematics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto

  4. Department of Psychiatry, Radiology and Public Health Faculty of Medicine University of Santiago de Compostela, Santiago de Compostela, Spain

    Torres Angela

Authors
  1. Jian-jun Jiao  (焦建军)
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  2. Lan-sun Chen  (陈兰荪)
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  3. Juan J. Nieto
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  4. Torres Angela
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Corresponding author

Correspondence to Jian-jun Jiao  (焦建军).

Additional information

Communicated by GUO Xing-ming

Project supported by the National Natural Science Foundation of China (No. 10771179) and the Emphasis Subject of Guizhou Province of China

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Jiao, Jj., Chen, Ls., Nieto, J.J. et al. Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey. Appl. Math. Mech.-Engl. Ed. 29, 653–663 (2008). https://doi.org/10.1007/s10483-008-0509-x

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  • DOI: https://doi.org/10.1007/s10483-008-0509-x

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Chinese Library Classification

2000 Mathematics Subject Classification

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