State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-03

AUTHORS

Sanyi Tang, Robert A. Cheke

ABSTRACT

A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour. More... »

PAGES

257-292

References to SciGraph publications

  • 2004-04. The effect of seasonal harvesting on stage-structured population models in JOURNAL OF MATHEMATICAL BIOLOGY
  • 1996-12. On the LambertW function in ADVANCES IN COMPUTATIONAL MATHEMATICS
  • 2003-05. Multiple attractors in stage-structured population models with birth pulses in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2000. Qualitative Theory of Hybrid Dynamical Systems in NONE
  • 2000. Success in Biological Control of Arthropods by Augmentation of Natural Enemies in BIOLOGICAL CONTROL: MEASURES OF SUCCESS
  • 2002-02. Density-dependent birth rate, birth pulses and their population dynamic consequences in JOURNAL OF MATHEMATICAL BIOLOGY
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    URI

    http://scigraph.springernature.com/pub.10.1007/s00285-004-0290-6

    DOI

    http://dx.doi.org/10.1007/s00285-004-0290-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1032473585

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/15480671


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