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Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects

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  • Pang, Guoping
  • Wang, Fengyan
  • Chen, Lansun

Abstract

Based on the classical stage-structured model and Lotka–Volterra predator–prey model, an impulsive delayed differential equation to model the process of periodically releasing natural enemies at fixed times for pest control is proposed and investigated. We show that the conditions for global attractivity of the ‘pest-extinction’ (‘prey-eradication’) periodic solution and permanence of the population of the model depend on time delay. We also show that constant maturation time delay and impulsive releasing for the predator can bring great effects on the dynamics of system by numerical analysis. As a result, the pest maturation time delay is considered to establish a procedure to maintain the pests at an acceptably low level in the long term. In this paper, the main feature is that we introduce time delay and pulse into the predator–prey (natural enemy-pest) model with age structure, exhibit a new modelling method which is applied to investigate impulsive delay differential equations, and give some reasonable suggestions for pest management.

Suggested Citation

  • Pang, Guoping & Wang, Fengyan & Chen, Lansun, 2009. "Extinction and permanence in delayed stage-structure predator–prey system with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2216-2224.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2216-2224
    DOI: 10.1016/j.chaos.2007.06.071
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    References listed on IDEAS

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    1. Wang, Fengyan & Zhang, Shuwen & Chen, Lansun & Sun, Lihua, 2006. "Bifurcation and complexity of Monod type predator–prey system in a pulsed chemostat," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 447-458.
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    Cited by:

    1. Jiménez, María Fernanda & Blé, Gamaliel & Falconi, Manuel, 2022. "A biocontrol agent as a commensal in a plant-pest interaction," Ecological Modelling, Elsevier, vol. 468(C).
    2. Wang, Fengyan & Kuang, Yang & Ding, Changming & Zhang, Shuwen, 2013. "Stability and bifurcation of a stage-structured predator–prey model with both discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 19-27.

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