Abstract
Abstract Taking into account that individual organisms usually go through immature and mature stages, in this paper, we investigate the dynamics of an impulsive prey-predator system with a Holling II functional response and stage-structure. Applying the comparison theorem and some analysis techniques, the sufficient conditions of the global attractivity of a mature predator periodic solution and the permanence are investigated. Examples and numerical simulations are shown to verify the validity of our results.
Highlights
The Food and Agriculture Organization of the United Nations reported that, with the development of modern science and technology, many methods have been used for pest control, such as chemical pesticides and biological control
Great progress has been made in the Integrated Pest Management (IPM), people still cannot completely exterminate them all
Some authors [ ] proposed an IPM predator-prey model concerning periodic biological and chemical management. It implied that the chemical pesticide is the most effective method which can eliminate a great quantity of pests in a short time
Summary
The Food and Agriculture Organization of the United Nations reported that, with the development of modern science and technology, many methods have been used for pest control, such as chemical pesticides and biological control (i.e., suppress the pests by natural enemies). Based on the above discussion, in this paper, we consider a stage-structured preypredator model with Holling II functional response and impulsive catching or poisoning the immature prey and stocking of the mature predator as follows:. In Section , sufficient conditions for the global attractivity of a mature predator survival periodic solution are obtained. This means that there is a positive periodic solution u∗(t) = c d pe–d(t–nT ) – – ( – p)e–dT. Applying the comparison theorem of the impulsive differential equation [ ], there is a n ∈ Z+ and a sufficiently small positive constant ε such that y (t). It follows from the comparison theorem that, for sufficiently small constants ε > , there exists t > , such that y (t) ≤ z (t) + ε for all t > t.
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