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Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay

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  • Chao Liu
  • Qingling Zhang
  • James Huang

Abstract

A harvested prey-predator model with density-dependent maturation delay and stage structure for prey is proposed, where selective harvest effort on predator population is considered. Conditions which influence positiveness and boundedness of solutions of model system are analytically investigated. Criteria for existence of all equilibria and uniqueness of positive equilibrium are also studied. In order to discuss effects of maturation delay and harvesting on model dynamics, local stability analysis around all equilibria of the proposed model system is discussed due to variation of maturation delay and harvest effort level. Furthermore, global stability of positive equilibrium is investigated by utilizing an iterative technique. Finally, numerical simulations are carried out to show consistency with theoretical analysis.

Suggested Citation

  • Chao Liu & Qingling Zhang & James Huang, 2013. "Stability Analysis of a Harvested Prey-Predator Model with Stage Structure and Maturation Delay," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, May.
    • Handle: RePEc:hin:jnlmpe:329592
    DOI: 10.1155/2013/329592
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